5/12/2011: Everyone's opinions change over time, and mine have as well. Due to the recent nerfs to Karthus, as minimal as they are, I have made some edits to this guide, such as the item order, rune suggestions, and overall things in general. Karthus' ult has been nerfed to a 0.6 AP scale instead of 0.7. This has changed nothing. I am still getting as many kills as I was before. Do not let this worry you. It means a difference of about 50 damage at late game.

03/16/11: Changed my opinion on the item order. As of late, I have had much more success with getting the Tear of the Goddess as the third item, then getting the hourglass next. I finish the archangel's later on as well, noticing I get better results from getting Rabadon's first.

03/09/2011: Emphasized my point on Clairvoyance. Updated the laning partners: Kayle, Kennen, and Malphite. Thoughts, theories, and general knowledge of Karthus as a jungler coming soon.

03/02/11: Changed the name of the guide cause it sounded better this way. Also updated my opinion on Mejai's vs Morello's due to the 20% cool down reduction buff that Morello's got.

02/28/11: Updated the guide with a section talking about all of Karthus' possible middle lane opponents. If there are champs that others feel I missed, or should be mentioned, please say so in the comments section below.

02/25/11: Updated the guide with a section talking about Requiem counters. Thanks goes to Crazy Smurf for the idea.

Hey there. If you're interested in Karthus, you've come to the right place. However, there are some things we need to get out of the way first if you want to play him. Karthus, unlike the other mages, is quite possibly the hardest mage to play effectively. So if you're looking for someone who can blow people up easily with a few button presses, play someone like Annie, Anivia, Veigar, or Ryze. Those are the ones who do that. You should definitely play Karthus if...

+ You enjoy killing numerous people at once
+ Enjoy playing offensive support
+ Have a lot of patience
+ Are good at predicting player movements

You should not play Karthus if you are not okay with...

- Dying a lot
- Getting ganked a lot
- Being focused a lot
- Staying in the back till the right moment
- Needing a blue buff to keep Karthus useful sometimes
- A difficult character to play

If you're okay with all of this, go ahead and continue.

Now let's start with the pros and cons of Karthus

PROS
+ Highly damaging if left alone
+ Can attack while dead
+ Best minion farmer
+ Global ultimate that can kill enemy champs
+ Great offensive support
+ Great harasser
+ Main attack is an aoe with low cool down and mana cost

CONS
- Frail frail frail frail. Low HP, armor, and magic resist
- Gets ganked a lot
- Is often focused
- Dying is sometimes a strategy
- Needs a blue buff to be useful in some stages of the game
- Needs to be fed to be good sometimes
- Very slow walking speed

Now, as you can see, Karthus is a very hit or miss kind of character. If you can get going on him, he's an absolute horror for your enemies to deal with, and they will not like seeing him. On the other hand, if you find yourself becoming underleveled, dying a bit too much, or just in general not getting fed the way you need to be, you're going to start to become dead weight to your team. So play well, and try to screw up as little as possible. If you know how to use him, he'll be great, I promise.

Death Defied: Unfortunately as of recently, this skill has been nerfed, and no longer provides the 20% death time reduction. The skill also allows Karthus to cast spells now for 7 seconds instead of 8 seconds. This does not change Karthus' general playing style, so do not let this discourage you from trying the champ. Riot is probably trying to discourage Karthus players from suiciding, and trying to encourage them to survive, which is fine. Karthus can still suicide on occasion anyways, so this change means little.
Lay Waste: Karth's main attack spell. Unlike other casters, his main spell is ground targeted, so this means you can't do good damage with it unless you're smart with it. You can just run up to someone, 1, 2, 3, I win someone like Annie or Ryze can. Using Lay Waste means you need to put this where someone is going to be, not where they are. Yes, you do need to be a little psychic with this skill. Your enemy almost has a full second to run from the location your spell was placed at.

An example would be someone like Tristana. Say you're laning against her, and a minion of yours is almost dead. She's likely going to try and shoot it for her splash. You can predict this and lay a bomb where she's going to stand in order to get that shot off. Lay Waste takes a lot of practice, but if you can get good with it, you don't need your ult, and you don't need Defile. Good Karths can get kills with Lay Waste. Bad Karths cannot.
Wall of Pain: Karth's Wall of Pain is one of the greatest supports in the game. With such a low cool down, ridiculous range, and aoe capabilities, it's something to be feared. It is also the first spell of Karth's kill combo. Starting with this will just about guarantee that your Lay Waste will hit its mark.

You need to be smart with this one though(I think that applies to all of Karth's skills now that I think about it). It has a hefty mana cost early game, so trying to kill someone with any less than half your mana isn't worth the effort or risk involved. Another thing to remember about this skill is that it reduces enemy armor and magic resistance. This helps your team and yourself. So you not only slow your enemy down, but you also reduce their defenses, making it much more likely to be killed.
Defile: Defile is probably the one skill you need to keep the most attention on. While it is toggled off, you will restore mana if you kill an enemy. While toggled on, you will drain your own mana to create an aoe of steady damage around you. With high AP values, this skill is extremely dangerous to ignore. A skill like this forces teams to focus you down with a hefty risk.

When I say it drains your mana, it REALLY drains your mana. You will run out of mana extremely quickly if this skill is toggled on. This is why getting the blue buff is helpful to Karthus. It means that he can basically keep an infinite Defile up while your team beats the **** out of the other team. Combining this with Zhonya's Hourglass will seriously piss off your enemies as well. Defile will remain up and continue to deal damage while you are invincible. There is a good chance you will die, with or without Zhonya's Hourglass, but you will have served your purpose. I think your team can do just fine without you if you happened to ace their team.
Requiem: While this IS the skill Karthus is most known for... don't be stupid with it. People who know how Karthus works are going to try as hard as they can not to get low enough so Karthus can't just shoot them from wherever he likes. While it is definitely a great skill for Karthus, do not depend on it. You want to use it as a last resort, or use it in a good situation.

Some examples would be...

Situation A: The most commonly used way of Requiem, and the best way Karthus gets stacks for Mejai's, as well as free kills. Some enemy champ is low on health at the moment. Pop Requiem, watch them die.

Situation B: Suicide bomber. You run in with defile, pop the hourglass, weakening them as much as you can and spamming Lay Waste. Hourglass comes off, you die, you keep defile up, you pop a few more Lay Wastes, you pop Requiem. There's a very good chance a lot of people are going to die.

So, as you can see, Requiem is a great skill. But it's not a skill you can just pop whenever to deal damage. Do not just spam it whenever you like. You'll be laughed at, and honestly, it's just ******ed. Also, while this skill is awesome and can change the direction of a fight immediately, there are a lot of items and skills that can counter it. Watch out for these items and skills and make sure you have your enemies waste it. One very specific counter to the skill is Banshee's Veil. Keep an eye on it. Your opponents are banking on it.

Okay, so thanks to the comment Crazy Smurf made, I've decided to add a section detailing counters to Requiem, how to bypass them, and other such things enlightening you on it. I will go alphabetically down the list of every character who has a potential counter. Characters not listed here either didn't have a big enough counter in my opinion to warrant putting them here, or there's something someone else knows that I'm missing, in which case, please feel free to point my ignorance out. Without further to do, here we go.

Anivia

This is annoying as hell. Oh look, Anivia's almost dead. Nope. She turns into an egg, and she's fine. There's not really anything you can do about this, especially if she's already behind her turret and friends at this point.

Annie

Fire Shield. Her Fire Shield is a very straightforward counter to the attack. While it may or may not save her, fact remains it gives her more magic resistance for a much higher chance at surviving Requiem. If your magic penetration and/or AP is high enough however, the shield will not save her.

Blitzcrank

His passive shield will come up and be annoying to you. That's okay most of the time. If you stack high enough on penetration and AP, you can bypass his shield sometimes, if you wait for the shield to either disappear, or decrease its protection by a bit.

Dr. Mundo

His ultimate, Sadism, popped at the right moments will save him. However, he has to pop it at very specific opportunities, or it isn't going to save him. If he waits until he has barely a sliver of life left, and you cast Requiem, most of the time there's nothing he can do about it. If by some chance though he had JUST enough for you to kill him without using Sadism, he's going to get away. Watch to see if he has used Sadism recently to get a kill.

Galio

I suppose his counters are pretty obvious. Bulwark and sometimes Idol of Durand used at the right moments can save allies. Of course, Bulwark is usually the better counter to the attack, but again can be penetrated if their health isn't TOO high and your AP is ridiculous. Sometimes though, Galio's a major problem.

Gragas

His passive, combined with his Drunken Rage skill heals him quite a bit, and since a lot of Gragas are sturdy, it's hard to get a kill with Requiem on him. Watch to make sure he has used Drunken Rage, or has already used it before trying to kill him with it.

Janna

Eye of the Storm and Monsoon. Eye of the Storm makes a shield, so that's an obvious counter. Countered in the same way as the majority of shields out there. As for Monsoon, not a TON you can really do about that one, unless you already know that Janna has used it recently and won't be able to use it for protect herself or anyone else for that matter. Honestly though, it's not too hard to get Requiem kills on her.

Karma

Same as usual. She has a shield she can cast, so that can easily protect someone. In addition, she has a heal spell that heals for a decent chunk. At least, a chunk big enough to survive you. In Karma's case, you either won't really be able to kill her with Requiem very often, or you'll have to kill units that are a bit away from Karma. Regardless though, it's very possible to get her with it, just as usual, make sure she's used her moves very recently.

Kassadin

Rift Walk. Nothing you can do about this one. If he times it right, you won't hit him. Case closed.

Kayle

Divine Blessing and Intervention. Intervention is the big one. No damage for a while is a huge hindrance to you, and she can just pop it if she seems the nice big glowy beam above her head. Divine Blessing is another obvious one.

Lux

Surprisingly enough, she has one of the smallest counters to your Requiem, and 9/10 times(at least for me), it doesn't save her. It's the shield boomerang she tosses out. Prismatic Barrier.

Maokai

His passive can get him lucky. And his ultimate is actually quite nice for reducing damage as well. Thankfully, everyone outside of the circle does not get the reduction, so what you can do as a team, is try to make sure they don't stay within that circle. Play cleverly with this one.

Master Yi

Meditate will save him often in some circumstances. For example, if you're chasing him, he's almost dead, and almost to a turret, and you hit Requiem, and he uses Meditate on reaction, there's a good chance he'll live. On the other hand if your team is chasing him and he doesn't have time to sit still, he's stuck. He either turns around to your team and faces certain death, or awaits the beam above his head to kill him. However, if you're the only one who he has to worry about, there's a chance that if Requiem isn't strong enough, he'll live.

Mordekaiser

His passive. His is one of the weaker shields in the game however. It's a nice constant shield to have, but you can knock away the whole shield quite easily and effectively. You'll need Mordekaiser to be a bit lower than usual though.

Morgana

Black Shield. She has one of the most annoying, if not, THE most annoying counter to Requiem in the game. She puts up a magic shield around someone. If she does this, I can promise you, you're not killing them. Requiem isn't strong enough to get through that shield at all. If Morgana is close to your Requiem target, give it up. You'll just be wasting it.

Nasus

His ultimate. Fury of the Sands can save him if he's willing to pop it to survive. If he doesn't have enough health though, Requiem will get through. Be cautious about this one.

Nidalee

Primal Surge for obvious reasons. You can still get some kills on her though.

Nunu

He's one of the more annoying ones. Say he's running away, and happens to run into one of your minions. Suddenly he gets a lot more health, and he ends up surviving your Requiem. Yeah, it's aggravating at times. All you can really do about this one is be sure he isn't near any enemy units that he can just gobble up. If he isn't, you've got a kill.

Poppy

Diplomatic Immunity. Nothing you can do about this one. She can interrupt you if you're close, and even if she's far, she'll just pop this. It's very very difficult to get Requiem kills on Poppy.

Rammus

His Defensive Ball Curl will save him sometimes. Predict it. Why would Rammus not use it if he thought he could get away if he used it? If he happens to use it, wait until it wears off to kill him. Regardless though, getting Requiem kills on Rammus is rare, and to be fair, the Rammus player probably isn't that good if he let you kill him with Requiem.

Renekton

Similar to Nasus, he can pop his ultimate to keep himself alive.

Shaco

His ultimate can save him in the same manner as Kassadin's can. He has to time it right however, so it's all up to him whether or not your Requiem hits.

Shen

He's a hard one to pin down. And he's good at protecting someone who can die to your Requiem without his help as well. Try not to get upset if he happens to protect someone, there's not much you can really do about it. Feint adds some problems as well. Shen is difficult with Requiem. Like most tanks, he will require a little bit of effort to kill off.

Sion

Like most shields, Death's Caress. And as usual, you can either wait for it to disappear, or you can hit through the shield and do enough damage to kill him if your damage is high enough. Weigh it up.

Sivir

She is honestly one of the most aggravating ones in the game for me. She has Spell Shield. With such a low cool down, it's extremely unlikely you will ever get the cast off successfully on her, unless she was in a team fight and popped it like right before she got away successfully. What's worse is that I've seen a lot of Sivirs who actually like to have a Banshee's Veil on top of it.

Soraka

Astral Blessing and Wish. She's a healer, and she's pretty much never out of mana, so it's unlikely to kill her with Requiem. Her heals will out heal you in time so she or whoever she heals, survives.

Taric

Same issue as Soraka. He can heal himself, and for quite a bit when he's alone.

Tryndamere

This one is kind of funny really. One of two things are going to happen. He's either going to get greedy and pop his ult to get on turrets or your allies like a lot of Tryns do, and spin away, leaving him vulnerable to Requiem. Or... he might save it for your Requiem, which I've also seen a lot of Tryns do. Tryn is both easily countered by Karthus, and Karthus' direct counter at the same time. It's all about how Tryn uses his ult.

Udyr

Turtle Stance sucks. Seriously. He's already really strong and sturdy. Turtle Stance makes it a lot worse. It's not likely you'll kill him with Requiem. Ever.

Urgot

Terror Capacitor and his ult. Urgot is good at avoiding Karthus if he's smart. Fortunately, if Karthus is smarter, you can get around it. Be patient, and don't be stupid.

Vladimir

This is one of Karthus' most well known counters, and I run into it frequently. Sanguine Pool is a much more reliable way of avoiding Requiem than say... Kassadin or Shaco's ults. Since it lasts for a decent amount of time, he can do it on reaction, pretty much. Not a ton you can do about this one, best to use Requiem after he has used Sanguine Pool.

Warwick

If he can use Hungering Strike, combined with his passive quick enough, he might live. It's rare though, Warwick is usually not a problem for Karthus.

Zilean

Not a darn thing you can do about Zilean's ult. Zilean's ult basically guarantees an ally's survival. If you see him use his ult on someone, don't even consider that person a target for Requiem anymore.


Okay, I think that about does it for Requiem counters. There are some other characters on my mind that I think may or may not be able to avoid Requiem, but I'm not positive, so I'll have to look into it. One in particular was Twisted Fate with the use of Gate. But I've never played him, so I would like someone else to answer me on that one.

It should also be noted that Banshee's Veil as well as Flash can avoid Requiem as well. Flash obviously has to be timed very well, but I'm told it works by a lot of people who fight other Karthus frequently. As usual, comments, tips, and other helpful notes are greatly appreciated.

Okay, first off, I believe for 5v5, teleport and flash are THE skills to get for Karthus. There are no other skills I would rather take than those two. Teleporting to minions and turrets, as well as wards, mushrooms, and Shaco dolls is just too handy. Flash is on there for very obvious reasons. Great for getting away, great for getting in, great for chasing. It's incredibly valuable to a team.

Now, as for the other summoner spells. I'll go through those and explain why or why not to take them.

Exhaust: Flash and Wall of Pain does everything this tries to do, better. While Exhaust is good for some characters, it is not good for Karthus. Reasons being, he's not a soloer, he's a team player. He also should be carrying Flash. Third reason being, he has a slow spell as it is. You don't need another one. That's just complete overkill. If you and your team know what you're doing, Wall of Pain is pretty much all you will ever need.

Ghost: Flash. It's better. You're not a melee, nor are you a fast running character. Same logic applies to this as it did to Exhaust. Flash and Wall of Pain is all you need to really chase or run.

Heal: No. There's a good chance you'll die a lot in a team, depending on how things are going. That, and Heal does not scale very well. You're also not a healer or defensive support. Leave this to the tanks and the healers.

Revive: Death Defied. Waste of a spell.

Smite: You're not a jungler. Leave it to a better character.

Cleanse: Again, you're not a melee. If you get focused or get a status effect, you're likely to die anyways. You may not even get the chance to pop this. This is not worth the spell.

Fortify: No. Leave this to someone else like a tank or support.

Clarity: I see this in a LOT of Karthus builds. Though, initially I could have seen why. I personally think it's not worth it. It's never really helped me since Karthus has Defile, and often times gets the blue buff, on top of the new Morello Tome and already existing Archangel Staff, Clarity is a waste of a spell.

Some people I'm sure though will argue its good use in early game. Yes, it has plenty of use in early game. Though, you can easily do without it in early game if you know how to play carefully, and try not to get too greedy. I've won plenty of games without it, and I often find myself losing games when I actually decide to use it. I advise against this spell.

Ignite: A good early game spell...... for easier casters. Since none of Karthus' spells are direct ones, killing people early game can sometimes be hard. Getting Ignite isn't really going to make it any easier. Leave Ignite to someone who can make better use of it. Like Annie, or Ryze.

Rally: Not worth it. It could be funny to backdoor with it on Karthus, though I wouldn't really recommend it. It's not worth ditching Flash so you can backdoor with Teleport and Rally.

Clairvoyance: This was a skill I liked a while ago. I no longer do, as it isn't showing itself to be useful anymore. People who know how it works, and know what it looks like always just change what they're doing anyways, or use it to their advantage to gank you. Sometimes not knowing is a better idea. I would never recommend this on Karthus. I would only say very few support champs could consider this spell.

Update: Case and point, I just had a game recently where the enemies used Clairvoyance to see who was at middle lane at the beginning of the game. It was me of course, so I walked around their eye for a bit. After it disappeared, instead of staying at the lane, I went to top lane. Since the enemies saw me at mid, they're not expecting me. I went up there, helped my two members gank and get first blood on two people, then teleported back to middle lane to protect my turret. Got me 1 kill and 1 assist right off the bat.

Okay, I'm going to be honest and say that people put too much importance on runes. Masteries are important for sure, but runes are more of an early game help than anything else. Most runes won't make much of a difference the further you get through the game.

Masteries

Update: 5/12/2011.Masteries, I took the obvious 9/0/21. Masteries have switched up a bit, albeit not much. I suggest the movement speed buff now for several reasons. Although small, it'll let you catch up those who did not take the passive, and will allow you to help your team better by placing walls sooner. The mana increasing mastery has also been removed. The reason for this being is that I found myself getting much more damage, and better results in general starting with a needlessly large rod, and then depending on how fights and such go, I can weigh up whether Zhonya's Hourglass or Rabadon's Deathcap will be a better choice at the time.

Runes

Update: 5/12/2011. Don't get too hung up over runes. They're mostly early game buffs, and you'll hardly notice them by late game. I usually go full AP runes, but lately I've been trying other things out due to Karth's recent nerfs. A full magic pen rune page works significantly well for Karthus. If you're running a full magic pen page, and start with boots, then grab Sorcerer's Shoes shortly after, you'll be able to penetrate practically anyone's magic resistance completely.

Other runes that work are obviously AP, health(flat, not per level runes), and mana regen runes. The only ones I will not suggest at this point are cool down reduction. Karth's skills are up more than enough, you don't need the extra cool down reduction. It is complete overkill, and will take away from runes you could be using for AP or magic penetration.

Everyone is a good partner for Karthus, but some are better than others. I will go through every single champ, one by one, listing which ones are best. The more *'s next to their portrait, the better the synergy.
***
Akali - She's a good one. She has good dps, and can hide if things get bad. She's a decent laning partner. Although, since all she can really do is damage, Karthus has to back her up a lot of the time.
***
Alistar - Not bad at all. Alistar, unlike Akali, has good stun and annoyance to teams. He can add that extra little push to your laning that you might need. Also, if you need to back up and run away, he can keep them busy since he's so incredibly sturdy.
***
Amumu - Amumu is interesting to do things with. His stunning makes laning a lot of fun, and makes Karthus' job easier as well. After all, the longer they stay stunned, the more you can use Lay Waste without predicting their movements.
*****
Anivia - She makes things tough for anyone, especially early game... which meeeeeeeans, Karthus' job becomes a lot easier as well. With her ultimate pretty much being up 24/7, that means your opponents will almost always be slow at one point or another. This makes using Lay Waste a lot easier as well. Stack it with Wall of Pain, and you can be sure they aren't running away from you. Anivia and Karthus compliment each other.
*****
Annie - Annie is a fun little partner to be with. If the Annie knows what they're doing, the person playing Annie will know to set up stuns for the right moment. Without Karthus' help, Annie is a huge threat as it is. So having Karthus' Lay Waste, Defile, and Wall of Pain added to the equation of Annie's stun aoes and overall ridiculous damage output goes a long way. A very dangerous duo.
****
Ashe - Ashe is an obviously good choice for laning with. Her ultimate, and her general AD, coupled with slowing is very advantageous for Karthus.
*****
Blitzcrank - Karthus + Blitzcrank = DEATH. It's a general consensus that Blitzcrank makes anyone's job worlds easier, but Karthus more so. Since Karthus' main attack is Lay Waste, Blitzcrank will give you free kills, even if Blitzcrank doesn't kill the enemy. They start to run away, you Wall of Pain them, and that's a dead person right there.
****
Caitlyn - She is not unlike Karthus in the aspect that she can lay traps to help support, and she can finish off opponents that think they're getting away. In addition, in the unlikely case that her attack doesn't finish someone off, you can do it for her with Requiem. These two make a very good team.
****
Cassiopeia - She's a fun one to lane with. Her poison is very helpful for you, actually. Having played with one a bit recently, it was interesting to lane with her. Your wall makes her poisons and her major abilities easier to land, safer to land, and hit harder all at the same time. Couple Wall of Pain's speed reduction with your Lay Waste, and the two of you will hurt quite a bit.
***
Cho Gath - Very similar to laning with Alistar, honestly. There isn't much difference between the two of them when laning with Karthus, save for Cho Gath silencing people. He's not a bad choice to lane with. But then again, when is a tank a bad choice to lane with?
****
Corki - This one, while not seen often at all, is actually a similar partner as to Ashe or Caitlyn. If anything, actually I might say he's better than the other two. He harasses like a mother *****, and with you supporting his advances, both of you should get some easy kills.
***
Dr. Mundo - Take this one with a grain of salt. Maybe I've just played with bad Mundos, but everything I play with a Mundo, we usually do about average at best. Kills don't come often for either of us, but we harass pretty well. Although, if someone is informed of something I'm not, please feel free to comment. I'll take your comment and add it if I think it might help everyone.
****
Evelyn - It's not likely this'll happen very often honestly. Most Eves jungle, and really that's how they should be. In the unlikely case though you do lane with one, consider yourself blessed... if they play well. Eve is very annoying to fight against, and since Karth makes a good top and bottom solo laner against two enemies, having her sneak around to help you kill people is really helpful to have.
*****
Ezreal - The two of you really complement each other. Since Ezreals need really good aim to actually do anything with him, you make his job a lot easier with your skills, and I mean all of them. Between Lay Waste, and Ezreal's attacks, the opponent is treading on land mines, basically. Also, Ezreal can help finish off opponents with his teleporting move to help you with Requiem, or to even save it for a better situation.
****
Fiddlesticks - While the majority of Fiddlesticks jungle, there are the occasional Fiddles that prefer to lane with a partner, which is all well and fine. Fiddlesticks can bring a lot to help you out. Ironically, casters in general seem to complement each other, as Fiddle and Karthus do as well. Between the two of you, being caught between Lay Waste, Fear, Drain, and Wall of Pain with Defile is going to hurt like hell.
***
Galio - Like most tanks, he's not bad. But to be honest, I'd rather have a different tank with me. Galio, unlike the other tanks, is slowwwwwww to being useful. It takes him a very long time before he actually begins to shine, and really demands a good player to be any good. It's not to say he's bad, he's not bad at all, it's just that there are often better choices as far as tanks go.
***
Gangplank - Average. It's not bad, but there's not a lot to really say about this duo that shines.
***
Garen - Don't make the mistake of thinking that I'm giving Garen himself a 3. Garen's a good character, no doubt about that. However, his options leave much to be desired when accompanied by Karthus.
***
Gragas - Nothing special here people, move along move along. He really only has his exploding barrel to help push people into you and your spells. Outside of that though, he'd be better off laning with someone else.
*****
Heimerdinger - This team is annoying as all hell. Heimer by himself is a real pain to deal with when played right. His turrets make everything a lot harder by themselves, and he banks on this. The two of you are outright annoying, and can harass like no other. Take advantage of it.
***
Irelia - Also take with a grain of salt. While I have never actually laned with Irelia, I have played her a lot, and have had her on my team quite a number of times, so I know how she works. I imagine laning with her isn't much different from laning with Akali.
****
Janna - This is actually a pretty neat duo. You help her a lot more than she helps you. You make her tornado easier to hit with, using Wall of Pain, which will combo into free Lay Wastes for you.
****
Jax - Jax is always bad to fight against, and laning with him with help give him free kills. You will of course make his job a lot easier with Wall of Pain and Lay Waste. Being scared of Jax, your enemies will often run very predictably, which will allow easy kills on your part. A team not to be underestimated.
***
Karma - I imagine this team would actually be pretty decent. Maybe even really good with her slows coupled with your own. Only thing is though, I've never laned with her, and 9/10's of the Karmas I run into are really bad, and it's beginning to make me think she's not too great of a support as someone like Sona or Soraka. However, if someone has more experience with this, comment like always.
****
Kassadin - Don't start thinking "OH WOW, THEY MAKE A GREAT TEAM" cause they don't complement each other. The only reason this gets a high rating is because Kassadin is broken as hell, and coupling ANYONE with him makes his laning team extremely hard to deal with, and has to be taken very carefully. The only way you really complement him is with Wall of Pain, but that's kind of a dur.
****
Katarina - Stuck between a rock and hard place pretty much. Katarina being the teleporting knife throwing, doom bringing assassin of hell she is, suddenly the world doesn't seem so bad to her when you're with her. Her ult and her knife throwing becomes easier with you for obvious reasons. Then you just assist her with your offense as well.
****
Kayle - Not bad whatsoever. She can help you farm a lot quicker with her attacks, and she's a great supporter and harasser for you. Definitely someone you should be happy to lane with.
****
Kennen - Well, I've laned with him a few times now, and I have to say, it's good and all, Kennen has great damage obviously, but he lacks the cc and utility that Karthus would appreciate from a duo. I'd personally perfer a different caster if I had to take one. Maybe Ryze or Annie.
****
Kog Maw - Cute little terror. Anyways. You both have annoying scouting aoes, as well as slows. You both complement each other. A good duo.
****
Le Blanc - While I've never laned with her, I have fought her a lot. I imagine these two make a very destructive duo, since Le Blanc can force people to run away. If they're weakened enough, it should make for some easy Requiems.
****
Lux - These two are hilarious. I mean really. She is just as annoying of a scouter as you, if not, more so than you. With her aoe scouting, her rooting, as well as her double rainbow beam of doom, you should be able to get some good kills out of the duo. Rooting someone in place means you don't have to think where to put your Lay Waste.
****
Malphite - Very good duo. I've had the opportunity to duo with him a lot lately, and I can say they work great together. His slow and his ult combine really well with you, and make kills mind numbingly simple to obtain.
*****
Malhazar - This is stupid sometimes. Malzahar, after he gets his ult, will net free kills between the two of you if he knows how to play right. While the enemy sits there, acting stupid, and getting their health drained, you just pop Lay Waste on them until they're dead. Very deadly combo. His silence and little summon help as well of course.
***
Maokai - Subject to change since he's still very new, but I'll give my general opinion on him. His saplings are annoying, and I really never got many kills laning with him. However, we were able to harass and trouble the champs we were dealing with quite a lot, and were able to farm in peace for the most part.
***
Master Yi - Master right click combos with Karthus just fine thanks to Wall of Pain.
***
Miss Fortune - She does alright with Karthus. Her aoe slow gives Karthus a chance to try and kill the enemies with Lay Waste.
***
Mordekaiser - Mordekaiser can be a real problem to deal with early game. He's a very solid champ for solo laning, and can get some easy kills on his own without Karth's help. I would suggest putting him with someone else rather than Karth, simply because Karth is also a powerful laner, so someone more supportive should be with Morde.
*****
Morgana - When I think about it, she plays like a slightly more supportive and defensive Karthus. She can hold people in place longer than Lux, so that means more damage from you. Her shield will also save both of you in a lot of fights. This is a team you don't even want to bother with. Very good duo.
***
Nasus - My opinion of Nasus is not a very good one to begin with. I can't think of one match I've had where Nasus was anything more than underwhelming, which is really disappointing, because I believe the better players out there can make him shine. But as far as this duo goes, the two of you will be very good at killing minions with your aoe dots.
****
Nidalee - So anyways, Nidalee is annoying to begin with, with how she always pounces her way to chasing and pounces her way to run. She also has some really strong strikes, so you two make a pretty good team, and she doesn't have to always chase her enemies away if you're with her after all.
****
Nunu - Okay, since Nunu also has a slow, but doesn't really have the damage to back it up outside of team fights, you come in for a nice duo. As always, your slows combo nicely together to make sure the enemy has a hard time running away.
****
Olaf - While I've only laned with him once before, we raped face when we did. Olaf is incredibly strong, and more so with almost any type of help. He's similar to Jax in terms of power, in some aspects, better.
***
Pantheon - With the recent nerfs, it's hard to find people who play Pantheon anymore. I've never laned with one, and it's been a while since I've even seen one. However, these two should be a pretty solid combination.
****
Poppy - These two are fun. Her knockback and overall stupid balance of offense and defense should make your job relatively easy.
***
Rammus - While I am of the opinion that Rammus should stay exclusively jungle, some don't like the jungle aspect of the game. Because of this, I have laned with Rammus before. Rammus makes a good partner for just about everyone though, for apparent reasons. Even with all the little nerfs he's been getting here and there, he's still a solid champ, and should be able to net kills between the two of you.
***
Renekton - Not bad. But he has a conditional stun, so unlike some melees who can get free stuns, like Eve, he's not as good as some others. They're alright though, especially considering how durable Renekton is.
****
Ryze - Before, I would've given this a 5, simply cause Ryze is just easy mode burst mage. But recently he was changed, so it's been changed to a 4 until I can get a better idea how the changes are affecting him.
***
Shaco - Nothing to write home about. Shacos generally shouldn't be laning to begin with. In the case the Shaco does want to lane, I would not suggest putting Karth with him. I'd put someone else with a stun or someone carrying exhaust.
****
Shen - Not really a ton different from Rammus. He just has a slightly more unpredictable way to inflict taunts on enemies.
****
Singed - Most Singed build tank, and for good reason. Because of this, he works as a good laning partner as far as killing goes and making your enemies scared to get near your turret.
***
Sion - He's okay I suppose. The only thing he really has going to help you out a bit is his stun. It might net you a few kills.
***
Sivir - Your typical AD carry. She doesn't really have any way to improve the way you do things. Given, if the Sivir is smart, she'll know when to pop the ult. Use Wall of Pain to make this easier on her.
****
Sona - She's a surprisingly good harasser. Her Q attack has a stupid amount of range, and of course she can heal you up and speed you up in dire moments. A very sturdy team, I have a lot of good results from this duo. Oh how I love her.
***
Soraka - I wouldn't rate her as high as I would Sona. Her healing isn't much better than Sona's, and her main attack is good for minions, however not too great for dealing with enemy champs. Her silence is helpful though if you're up against ranged fighters.
****
Swain - He's a good combo if he lands his snare. His ult also makes both of you very intimidating.
****
Taric - Probably the best support partner you can have for your lane. He's like Soraka, but better since he has a stun.
****
Teemo - He's really useful for your lane. His poison, coupled with his mushrooms(assuming they hit) are really nasty. Running into a single mushroom can spell death for someone between you and Teemo.
****
Tristana - I was bordering on 3 or 4, but I gave her a 4 for being Tristana. Tristana isn't unlike Sivir in a few ways, except that she can actually slow people down(and usually does), and knock people back towards her team or turret(and she usually does that as well). Played right, this team is pretty sweet.
?
Trundle - Trundle shouldn't be laning. He should be jungling.
****
Tryndamere - Bordering on 5, Tryn makes it a lot easier for both of you to get kills. He already has an impressive slow in his arsenal, and stupidly high damage to go with it. Couple him with your wall and your damage output, and you got a very dangerous team going.
****
Twisted Fate - This shouldn't really happen to begin with... Twisted Fate shouldn't really be laning with you, as you're both really good mid laning champs, and chances are the one who got mid doesn't realize the usefulness of either of Karth or Twisted Fate's ults. But it is a solid combo, especially if he can land red or gold card.
***
Twitch - Pretty much the same as Shaco, except more frail and slower.
****
Udyr - I've laned with an Udyr before, and it's reaaaaally nice to have. While he doesn't have a ton of utility, he hurts like a *****, and is very sturdy. A nice team member to have to lane with.
***
Urgot - Meh... not very good. Urgot's good at chasing away. He's a great creep denier, but you don't exactly benefit from that as Karth.
*****
Veigar - Complete and utter overkill in my opinion. His aoe stun is ridiculously useful for both of you, and coupling that with Karthus' abilities makes it very potent. Considering Veigar's ultimate as well, it's not a team you wanna screw with.
****
Vladimir - He's a good choice to have for simple reasons. He's a very sturdy mage, and can deal out nice amounts of damage. A very good choice, even if he may not help you as far as utility goes, he certainly helps himself by being very evasive.
***
Warwick - Warwick should not be laning in the first place, as he's a good jungler. This is not a team I would recommend.
****
Xin Zhao - He's a good laner, and your wall should help ensure some kills.
*****
Zilean - This team is hilarious. Zilean's a good harasser on his own, and his ult is amazing support as well. His skill can be used to slow or speed someone up, so you can both chase and run. You both output great damage, and if one of you die, his ult is there to save you both.

Here, I am going to list every enemy that I believe that Karthus will, can, and may run into when it comes to soloing the mid lane. If there is a character that you have ran into and it is not on this list, that is either because A: the chances of running into them are extremely unlikely, or B: they're so easy for Karthus that it's not worth mentioning.

Anivia

This character is easy mode to play. Not play against, but to play as. Seriously. She's difficult for a lot of champs to lane against because of her slows and good damage. Even if you kill her, she'll turn into an egg, and be perfectly fine, especially if she was able to get behind her turret before she died. Play carefully, and keep your harassing to a minimum. When she hits level 6, keep a little more distance than usual and watch her mana. Her ult takes a lot of mana to use, but it's also very easy to use, and has an incredibly low cool down. If you get hit by it, there's a good chance you'll die without the use of flash to bail you out. This is a hard one for Karthus to play against at times.

Annie

Annie is a little easier to deal with than some champs. You both suffer from extreme squishyness and can't afford a mistake, so it's all a matter of who outplays who. Although you definitely wanna be very careful around Annie after she hits level 6 and has her stun ready. You can tell when she has her stun ready because there will be this little circular wind around her. Even at full health, a good Annie will kill you with one rotation of her spells if she has her stun and ult ready, so be cautious. Don't get any closer than you have to. Luckily for you, she is scared of you as well. If she doesn't have a stun ready, there's a good chance you can outdo her if you're careful about it.

Ashe

Not hard for Karthus at all. But you do need to be careful of a few things. Keep in mind that her normal attacks can and will slow you down if you get hit. Ashe is extremely easy to harass and if you play well enough, you can get Ashe killed once or twice before hitting level 6 if she gets a little too greedy. I've done this countless times. However, like I was saying, you need to be careful at level 6+. Ashe will have her ult at this time, and if she does hit you with it, there's a good chance she will kill you. So after level 6+, play defensively, ask for assistance with ganks, and hug your turret. Even if she can't kill you with her rotations and normal attacks, I can almost guarantee you that after hitting you with her ult, someone is going to help her gank you.

Caitlyn

She's actually not nearly as bad to deal with as Ashe is. There's not a lot to worry about from Caitlyn. She doesn't have any good methods to keep you in place(as long as you have eyes that can see traps), only her damage is her strong point. After level 6+, try not to let yourself get any lower than about half of your life. Her ult is really powerful, and being so super squishy, she can make quick work of you. Just don't get greedy, and use those eyes you have to see her traps.

Cassiopeia

She's really easy. I feel bad for her. There isn't really much I can say about her except for be careful when she's 6+. She'll petrify you and kill you relatively quickly, so keep your health high and your distance fair. Otherwise, she's not a big threat.

Cho Gath

This is one of Karthus' harder match ups. While Cho Gath doesn't hurt enough to be a threat to Karthus, he is a great harasser and will make harassing him a little difficult. However, I will say though, the match up isn't NEARLY as hard as most people make it out to be. I found myself laning against Cho Gaths pretty easily. The key is to just not get greedy and watch the floor intently. There will be a little warning on the ground before Cho Gath pops you up into the air.

Corki

He's an annoying one. Think of Caitlyn with more damage and no traps and that's what Corki is. While he doesn't really have a good way to get free kills, he hurts like hell, and his ult has pretty much no cool down. Proceed with caution, and do not harass anywhere near as much at level 6+.

Dr. Mundo

I've seen this more than I thought I would... but anyways, with Mundo, he doesn't hurt enough to be a threat to you. You can harass him as much as you like until about level 4. After that, don't bother. He just regens life way too easily, especially at level 6+. His ult makes hitting him a waste of time. Just farm around him and see if you can get your allies to help gank him.

Evelyn

Simple. She's annoying if you can't see her. This is why you're going to put a invisible ward down in your lane so you can see where she's at. She's not a big threat as long as you can see her.

Ezreal

He's... annoying sometimes, and other times laughable. It really depends. His attacks can be avoided if you move around a lot though, just be careful of his warping and his ult. Flash out of his ult at the last second. If you do that, you'll have enough life if you play intelligently to survive his next ult, and then flash the next. You wanna flash every other ult if you think you might not survive. Otherwise, Ezreal's not too hard as long as you keep moving around.

Fiddlesticks

Fiddle is easy up until level 3. By that time he has Drain, Fear, and silence all at his disposal. You can harass, but do it carefully and out of his range. See if he has flash too. If he has flash, you might not wanna try harassing. His damage and control will be better than yours when pitted up against one another. Have an ally help gank him. Regardless, he's scared of you too, so you'll wanna stick to just farming until someone helps you out.

Gangplank

He's easy. Not really anything worth mentioning. You can harass him for days and there's not much he can do you. Your damage output, control, and range are all better than his. His ult is the only redeeming thing he has going, and you can just flash out of its range if your health is low enough.

Heimerdinger

He is also really good at farming and harassing enemies. Take him down with caution, and save most of your mana for his tiny turrets. You want to take those down before you work on the minions.

Kassadin

Of all the enemies Karthus can potentially face at mid laning, Kassadin and Le Blanc are, in my opinion, his worst match ups. Kassadin has far too much mobility and damage to let you farm or harass the way you normally would. His ult makes getting damage and kills a breeze for him. He can be almost a little further than half a screen away, warp over to you, hit you with a silence ball, and run away. And he'll keep doing this over and over and over again since his ult has somewhere around a 3 second cool down. He is definitely the better harasser in this situation. Not only that, if he's close enough, he can warp over to you(damaging you), slow you with his aoe, silence you, and then in some cases, chase you until your death. He's excellent at avoiding harassing and escaping. He's one of Karthus' greatest counters for a game.

Katarina

You have to play against her pretty strangely... she's going to take advantage of warping over to you, knifing you, and then running away. So a good thing to do is put yourself at a minion, and set a Lay Waste there. So that way she warps into your attack, you can Wall of Pain, and lay into her a bit. Katarina's not too hard honestly, her damage is just intimidating at times.

Kennen

He's fast, but if you move around a bunch, he's not an issue. Just don't get greedy with him, he'll make sure you regret it.

Kog Maw

Not hard at all. Being AD(most of the time), he's not an issue. It's a general consensus that most AD champs aren't an issue for Karthus. Kog Maw's no different. Just make sure you move around a bunch when he gets his ult.

Le Blanc

Hate hate hate hate this one sooooo very much. More so than Kassadin. She is one of the very few champs that I will ask someone to switch with me on. Karthus is terrible at fighting her and Le Blanc players know it. She can warp, silence, duplicate, etc. She's extremely annoying to fight, and you'll be hugging your tower most of the time when fighting her. Either switch with someone or have your allies help gank her, cause you're going to need it. If you aren't running into problems fighting her, you're fighting a bad Le Blanc.

Lux

Lux is a pretty easy one. Since none of her spells are targeted, you can easily move out of the way of her spells. The only thing you have to worry about is getting snared, and then shot with her laser beam. You need to make sure this doesn't happen. A good Lux can harass a Karthus, but a good Karthus can harass a good Lux better.

Malzahar

He's not hard at all until level 6. At this point be very careful. His ult is stupidly easy to use, and its power combined with its suppression makes it even easier to kill you. If he hits you with it, he has a free kill basically. Just play safe at level 6+.

Miss Fortune

She has nothing on you. Harass her all day long.

Mordekaiser

Don't bother harassing him. I've had terrible results every time I tried. His little metal meter just makes sure you're wasting mana on him, when you could be better off farming the minions around him and using Requiem to kill people in other lanes. Have your allies coordinate a gank on him.

Morgana

She's not particularly powerful, but she isn't really weak either. She's in a boat similar to your own, in that she is great offensive support. She a move similar to your Defile, can shield herself(or an ally) from Requiem, and her ult can seriously hurt if you don't get away from her in time. Play cautiously. Morgana is surprisingly sturdy.

Nasus

Harass all day. You have very little to worry about. It's just his slow and his aoe attack that sometimes gets annoying, but he isn't a threat to you.

Nidalee

She can be annoying, but nothing more. You can harass her quite a bit. Just don't get hit by her spear. It hurts like hell. You should stay pretty close-ish to your turret with her.

Nunu

Harass all day. He's not a threat to you. He has a snow ball that slows you. It's no big deal. He doesn't output enough damage to break you. Watch out for incoming ganks, as Nunus I've played against more often than not, call out ganks.

Pantheon

Harass all day. He is also not much of a threat to you. The best he can do is jump on you and spear you a little bit. Just make sure that's all he does.

Ryze

This wasn't hard until the recent patch. Ryzes build tankish with mana items now to get the most out of Ryze. Personally, I think Ryze is now stronger than before. He has similar to, or slightly better/worse power than before, and he's worlds sturdier now. You can harass him quite a bit though, as it takes a while before he starts to hurt. As the game goes further and further though, you're going to find yourself falling behind. But that's okay, because by the time this starts to happen, you shouldn't be laning anymore anyways, and neither should he.

Sivir

She's easy. Just remember she has her spell shield. Do NOT pop Requiem if she gets behind her turret and she has not yet popped her spell shield. If she popped it a few moments before getting behind her turret, then it's safe. Otherwise, don't bother. She'll just block it and you'll get a nice little "lololol noob" message. Otherwise, she's no threat to you.

Teemo

9/10 times, I end finding out Teemo was close to the turret as possible to both avoid getting hit, and making sure he could hit you. In addition, he's usually stealthed, waiting for you to pop up so he can get an easy kill. It's a coin toss at this point whether you'll get him or not. If you're not stupid about it, he won't kill you, even if he gets the jump on you. Just pop flash and your health potion. A lot of Teemos get too greedy, and I usually find myself killing him instead. After the initial level 1 encounter, he's not much trouble. Just make sure you watch where his mushrooms were placed, and consider getting an invisible ward so you can see them.

Tristana

For a long time, she isn't any trouble at all. At level 6+, don't push too hard into her turret. If you do, there is a chance she'll jump over you, and ult you into her turret. So if you're going to get really close, be sure she's almost dead before trying anything so at the very very LEAST, you can take her down with you. Best case scenario, she shoots you into the turret, you kill her, flash over a wall away from the turret. It's just pushing too far and getting greedy that Tristana can easily bank on.

Twisted Fate

He's a fun one to play with. You both are quite good at harassing, so enjoy the little tit for tat game you're going to play with him. Watch his cards carefully. Wait until he has used his card before you try attacking him. You can harass him quite a bit, so make sure you do. But the moment a card is being picked, move away and wait until it's used up. You have the edge, but if he hits you with a card, he'll make sure you die. So avoid those cards.

Twitch

Similar to fighting Evelyn, only he's ranged and has poison. You don't have stuns to worry about thankfully, but you do have a slow to worry about, and his ridiculous AD(usually). But same strategy is applied. You can harass him a lot if you put an invisible ward down in your lane.

Veigar

Hoooooo boy... okay, for a long time, Veigar's not a problem. But after level 6 he becomes a HUGE threat. It's not his ccing or his raw damage output that's the problem. It's his ult. Since it will combine both your AP and his own for damage, it's almost a guaranteed one shot on Karthus if Karthus' AP starts to get really high up. Harass him like hell until level 6. Try to get help for ganks, try to get him killed, deny him as much exp and gold as you can. Once he hits level 6, unless you have completely outleveled him, keep your distance and tower hug.

Vladimir

Considering his recent nerfs, he's still really good, but he's a lot more tolerable now. His damage output isn't enough to harass or kill you without help if you're playing carefully. You should be able to harass him better actually. Just remember Sanguine Pool though. It's one of his best attacks, and a direct counter to your ult. If you see him use it, back up and wait until he pops back up.

Okay, I'll explain how you should start each fight, and how you should progress through the game as it goes along.

So, first of all. Debate with your team who is going to take the mid path for laning. Generally, people accept that Karthus is a very good solo laner, so there are few champs and people in general who will try and take mid away from you. There are some champs though that you should definitely let take mid laning instead of you, especially if you meet 1 of 3 champs at your lane.

If you meet Cho Gath, Kassadin, or Le Blanc, switch with someone else. These three are just going to get free kills off Karthus, are a waste of time to harass, or you'll have to play stupidly safe. Karthus has a lot of trouble fighting these three if the people playing them know how to play them and how to fight Karthus. Some slightly more annoying ones, but certainly nowhere near as hard as the aforementioned three include: Ezreal, Ashe, Katarina, Veigar, and Heimerdinger. The reason I put Veigar on there is because his ultimate makes Karthus a very easy kill, being as Karthus almost always builds full AP.

You should give up the lane to someone else if the person arguing for it is Ashe, Annie, Corki, Katarina, Kassadin, and in some cases, Nidalee, Vladimir, and Anivia. Regardless though, if these champs are on your team, and they don't argue it, take the lane. Karthus, after all, farms better than any champ out there, even if some of these champs may be more reliable or have some better utility.

Beginning the Game and Early Game

Update: 5/12/2011. Almost every game I play I start with Sapphire Crystal. The reason for this are a few. First of all, playing experience has taught me that 9/10 times, snowball items are not worth it. Especially in ranked play, as you will be focused down like mad. Dying can be a solid strategy for Karthus, depending on how well your team is doing and what you guys need at the current time. The other reasons for getting the sapphire crystal are that is is a great amount of mana, so it will let you spam Lay Waste a lot more. In addition, it will help you build Catalyst and Rod of Ages, which is going to be one of the first items you complete. Rod of Ages is not worth it unless you build it early.

Another starting item that can be good for Karthus is are boots. If you're using a full magic pen page like I sometimes do, then starting with boots, and getting Sorcerer Shoes first can be a great idea. It will let you penetrate just about 100% of anyone's magic resistance early game.

Now that you have done that, lane and take mid if you can. If not, find a good partner to lane with, or solo top if you have a jungler. Karthus does NOT have to always to take mid, though he is one of the best champs to take it. If you're laning well, you should not have to go back until you can afford catalyst and some boots or your Sorcerer Shoes. After grabbing those, make sure you keep an eye on the entire map for people to hit with your ult when you hit level 6.

Be careful with your ult. Have your team tell you when they see someone low, getting away, etc. You can also use this to help your team engage. Weaken the enemy team, and it'll give your team the edge they need to defeat their laning opponents. There quite a few ways to use your ult. Do NOT use it to steal kills. Use it to weaken the enemy team and kill stragglers. Do not use it to kill someone who is already going to die. That's a pain to your own team, and deprives them of gold. You are not the only one who needs gold.

Mid Game

By about mid game you should be close to finishing either your Rabadon's or your Zhonya's. Regardless, you now need to start being careful. The laning phase is pretty much over at this point, and if you've been doing a good job, you can be sure the enemy team hates you. If they're smart, they'll focus you from now on in fights and build magic resistance to counter you. Keep an eye on what they're building. If you see them starting to build banshee's, and other magic resistance gear, you should consider building a void staff very soon. It'll go very well with your Zhonya's and/or Rabadon's.

If they're not, and they're building pure damage, then you can start building on a Zhonya's if you haven't already, a Rabadon's if you haven't, and if you have both already, then you should start working on Rylai's. This is great for Karth. It'll give him the extra survivability he needs, as well as a movement impairing effect to his spells. This'll be extra valuable to your team on top of your already powerful wall of pain. Watch what your enemies are building though.

Another thing to mention. If you are running your team with a jungler who is constantly taking the blue, and constantly needs the blue, give it up. Let them have the blue. In this case, build Tear of the Goddess as your third item, right after Rod of Ages and Sorcerer Shoes. Do NOT build Archangel's until later. You're just getting the tear for now to help with the mana. Buying Archangel's Staff later rather than sooner is a huge money saver, and will help you much more in the long run.

Late Game

At this point, I would generally have a Rod of Ages, Sorcerer Shoes, Zhonya's Hourglass, Rabadon's, and Ryali's Scepter. By late game I would expect you to have the same. Rylai's is sometimes replaced by Void Staff depending on the enemy team's composition. Your last item should definitely be something along the lines of Ryali's or Void Staff though. When you're finished, your build should be something along these lines:

1: Rod of Ages, Sorcerer Shoes, Zhonya's Hourglass, Rabadon's Deathcap, Rylai's Scepter, Void Staff.

or

2: Rod of Ages, Sorcerer Shoes, Zhonya's Hourglass, Rabadon's Deathcap, Archangel's Staff, Void Staff.

Magic penetration is always better than Rylai's. You need to deal damage, deal it quickly, and harass like no other. You already have Wall of Pain, so Rylai's is not always necessary. Especially if you're fighting some champs like Master Yi or Olaf.

That's the majority of it. Some other helpful tips to remember are as follows:

1: Remember that all your spells are either aoes or ground targeted.
2: Because they are all ground targeted or aoes, you can be a great scout for bushes. Use Lay Waste and Wall of Pain to reveal enemies.
3: Always keep an eye on your allies as well as your enemies at every given point.
4: Gank top or bot if you're laning really well at mid. You are a superb support with your Wall of Pain. And even if you don't help your allies kill someone, it will scare off your enemy or force them to waste their summoner spells.
5: Don't be stupid XD