First of all, I am not a pro player and this is my first guide :). I saw this item sequence and play by TPA Toyz in the League of Legends season 2 world finals, which I wrote down but got tired of reading off a note of paper, so I made it into a MobaFire guide since they have a nice layout.

Second of all, this is TPA Toyz playing, meaning you will probably have a hard time keeping up with his play, (I know I have..) and his choices of items might be a little risky, eg. Blasting Wand, before finishing Catalyst of Aeons, although he's buying the pre-items for this.. but can do this because his team just won the world finals.

Thirdly, this is not for new players, you may practice by this and become a totally awesome Karthus player, but it's recommended that you've played Karhus before/read other guides/ have a (preferably more than) basic knowledge of his spells, the items, so on and so forth.

The game can be seen on the riotgames stream,
http://da.twitch.tv/riotgames/b/335762610

**As I have no idea of how he has set his masteries or runes, these will be STOLEN ( :O ) directly from the top build at the moment, King Killsteal since it seems like a good reference. So infinite ritches, fame and credit to that person!

oh and finally, please! discuss this, I can only know what I've been told or seen with my eyes, and as I said at first, I'm no pro player, so it'd be awesome to have some pro-eyes on this :)

The build starts with Boots and 3x Health Potion, cause all the players (not support) at the LOL Finals would start with this. Therefore it seems like a "pro" idea.

The build includes sight wards, cause all the players (at some times not the ad/ap carries).. -|| same as above ||-

He doesn't buy the Catalyst of Aeons in the Rod of Ages before the Blasting Wand, although he buys the pre-items for it, presumably cause he doesn't care about the survivability you get from the Catalyst of Aeons, but he's more interested in the flat bonuses from the Ruby Crystal and Sapphire Crystal + the damage output from the Blasting Wand.

After 14mins 30sec, He buys the Rod of Ages (162 minions killed)

In the 25th minute he buys the first Needlessly Large Rod (282 minions killed)

at 30 minutes he buys Rabadon's Deathcap (352 minions killed)

He ends the round having bought the Chain Vest, I assumed he wants to upgrade this into Zhonyas Hourglass which just goes plain awesome with Karhus' Defile AOE skill.

I can't say much about this, since I'm not a mad-pro-2000wins player.

But choosing Flash and Teleport gives an awesome movement advantage.

Flash
You can easily prevent ganks and save your behind whenever you're jumped, and you have the opportunity to go over a wall or alike. You may also use this for chasing down enemies for an extra kill.

Teleport
Saving that tower and preventing the other team from receiving a bounty of 750(150*5)gold is actually a pretty feat. You may also teleport to a ward surprise ganking from a bush or just getting quickly into lane after having recalled or died. More useful that I thought before trying it.

Alternative to Teleport you may want to choose Exhaust (AF RapidStar did this) which will help you chase down that puny lowlife champion trying to cower away with its tail between its legs, or just be better set when you're facing a champion you'd much like to miss a couple of attacks.

At all times he's ready to pop his Defile even for a single second, to snipe a minion he wouldn't get otherwise, you'll want to practice this.

At all times, when the wraiths are up, (and the wolfes) you'll want to go for these to increase your minion score (don't mess with your jungler if you have one of those!)

Already in lvl 1 he attempts (and succeeds) to steal the bigger of the wraiths in the enemy forest, by standing in range of its ranged attack and bombing it with his 875range Lay Waste bombs for ++gold.

He uses his Defile skill, to reach over the bush while he bombs the biggest of the wraiths, when he only wants to take out that one. (Notice this if you see the video, can't remember where it is shown, but it will happen....)

In lvl 7 (and 11 (no pun intended)) he goes for Golem.

At one point he pops his ulti Requiem for no kills, just to pile-on, on the damage that the two enemy champions in the bottom lane have received, they have to recall, and his bottom lane can push a tower giving 750 (5*150) gold to the entire team.

If you want to learn how to play better, watch pros play.

I can definitely recommend watching this match as well as the first match in the finals, with Azubu Frosts RapidStar playing Karthus. It is awesome.
http://da.twitch.tv/riotgames/b/335762489 <- RapidStar as Karthus

And as I wrote in the introduction, please, discuss!
-I can only know what I've been told or seen with my eyes.

Hope you might use this for something greater :)
-figaw