Pros-
Can pick up kills that can't otherwise be gotten
Great Damage dealer in team fights
Great support -magic resist/slow
Can fight after death
Aggravates the entire enemy team
Just being near an enemy means they might die

Cons-
Can be squishy
Tends to Level out late game
Can be shut down my magic resist if your team is AP heavy

This is my guide to playing one of my favorite heroes. Karthus is a champion that gets on alot of peoples nerves, mainly because they cant get past the one basic rule to beat him in the early stages of the game (Dont commit to an attack on Karthus unless a. you can kill him and get out. -or- b. you can live with the shame of an eye for an eye suicide pact.) Mid game, when the game turns into a team fight/gank fest, Karthus is most important of all. A champion that can die and continue dealing large amounts of damage can turn a loosing battle into a penta kill if the climate is right. Sadly Late game Karthus can fall apart, this is due to his amazing ability to out level the enemy and get all 6 of his items before any one else. The sad truth is once he hits this mark he will no longer get better but enemy champions will, so its up to the players skill to keep your team in the game.

-The most important rule to Karthus-
Dont piss off your teammates!
when in the course of the game you see the opportunity to press the R button and steal a sweet sweet kill from a team mate Do Not Do It. if your team mate fails to get the kill and doesn't seem keen on tower diving to finish the job then and only then should you use your most powerful ability.

This is on average my usual build for Mid Karthus. I rarely deviate from this exact build in this exact order. the few exceptions might be that I get before I get . Obviously if your having a tough time mid youll want to stalk up on some potions and if your getting ganked a Sight Ward or two wouldn't hurt. Towards the end of Mid game if you see players on the enemy team getting some magic resist a wouldnt hurt. I tend to ditch my or my if it looks like I'm playing defense and don't need to move from one side of the map to the other.
-Odds are at the end of most games my items will look exactly like this


The second build is a more aggressive style and thanks to some of the comments I have started getting Rylais a bit sooner.

These Summoner spells are my favorites for Karthus.

Early game Teleport allows you to get back to lane if your ganked or if your enemy lane partner decides to trade a kill for a kill. This can be the difference between hitting 6 early and getting a few more early game kills, and getting out leveled. Mid game Teleport can do almost anything help you get to team fights, push towers, pick up some minion kills in empty lanes, and even get you out of a hot zone faster that recall.

Flash for obvious reasons is one of the best summoner spells in the game. This spell will help Karthus cover one of his biggest weaknesses, his speed. closing the gap on an enemy that has flashed or ghosted can get Karthus many more kills with out needing to waste an ult. Just by walking along side an enemy Defile can pick up kills.

Some other options can be for more mana early game though I don't think this is needed due to Defiles passive. could help karthus make sure an off-screen enemy can be finished off by Requiem. And can be used in place of Flash but I don't recommend it if you have hit level 12 already.

In mid there 2 things will keep you alive above all other things communication with your team mates (I hope you are on Mics and can openly talk) and Line of Sight. Sight Ward and can both help with this. Sight Wards should be place in the side bushes along the river. Never under estimate however what the spell Lay Waste is capable of however. It has a massive range and temporarily reveals the area in which it explodes. Due to its low mana cost, short 1 second cool down, and its range, you can easily check any bush that might have ganks waiting.

If a Teemo is on your team have him place shrooms instead of sight wards. 2 reasons 3 mins < 10 mins, and if you need to get away a shroom and slow and maybe even kill a enemy champ.

Early game Farming Consists of using to lay into waves of minions.
Some of the most important things to keep in mind for this stage is placement of this spell. Because lay waste has such a short cool down you can feel free to harass and farm minions with it. Its mana cost is relatively low and with the passive from you wont have to run out of mana (Last hitting at Level 2 or higher). try and last hit with your attack when you can (when enemy champs seem mia or near their tower). When minions spawn the walk in 2 groups of three generally 3 melee and 3 ranged. In the mid you only have to deal with 1 other player -unless ganked- so use lay waste at the back of the ranged minions to harass the enemy champ and damage 2-3 minions at a time. When the minions seem to be low use a lay waste to last hit and hopefully refill at least 2/3 of the mana used that wave.

-Do Not Use Defile to farm minions in early game- Instead only use defile for enemy kills. I like to Lay down a wall of pain on my enemy or behind them and tear into them with Lay Waste, if they live through 2-3 and seem like they might get away Flash and turn on Defile to finish the job.

Mid game -aka lvl 8-13 you should be picking up some points in defile and now you can sweep through minion waves.
Steps
1.Stand in between melee and ranged minions.
2.Turn on Defile
3.Hit melee minions with Lay waste
4.Hit ranged minions with Lay Waste (while aiming for cannon minion as well)

Late Game Farming is simple as you walk through anywhere if there is something you can kill turn on Defile and as you walk by it, it will die. While walking to help in team fights of ganks if you can see no minions in lane and you can go through the Jungle without taking up more time kill the wraiths and wolves with a well placed Lay Waste.

This is where Karthus Excels. When a team fight starts you want to be almost right behind the tank with this build. Keep in mind you do not have to live so if they focus you, oh well, you'll still kill some of them and help your team push the lane and win. Right when the **** hits the fan you want to find your target which might be as easy as The Group, and use Wall of Pain on them. Defile should probably be on already but if not Now is the time. Now If you have Zhonya's Hourglass and you are being focused you can activate it for 2 seconds more of defile damage with out being harmed. After the effect wears off you need to find your squishiest and weakest targets and hit them with Lay waste. keep focusing down all the players until every one is dead.

-If you die-
Now if things don't go perfectly, and they won't. don't fret. You can continue to kill and maim. Just remember Requiem has a delay. So if you think it is needed to finish off the entire enemy team, or it will do it faster, use it before grey out (the icon will grey out 4 seconds before Karthus has to stop fighting.) Rarely but some times when you ult when dead the game can glitch and waste your Ult, it can be frustrating but deal with it imagine how the enemy team feels when it works.

-If you live-
For obvious reasons this can be rare. I don't want to see any Karthus Flashing out of a team fight to save his skin, unless his team is dumb as bricks. But if you do live push the lane or complete what ever objective is in the best interest of the team.

To sum things up I will say be kind to the people you play against unless they start it.
-and don't KS -kill steal- a team mate when you know damn well they can get the kill.