This is my personal build that I use mostly for non-competitive play. Nothing too powerful, but quite nasty in group fights. For the most part, the build is designed for continuous drain in a fight with Defile while using Lay Waste on anyone standing alone. With Lich Bane, this leads to very powerful attacks (feeding off of his AP) and sustained combat due to high levels of mana and the 25% Spell Vamp given by Will of the Ancients.

-Be wary that the site does not add the Ability Power gained from Archangel Staff (3% of your total mana), making the AP levels shown greatly misleading.

Pros:
-High mana, making long battles easier
-Able to last a while on nothing but Spell Vamp
-Good for clearing out mass numbers of creeps

Cons:
-No real early-game ability
-First Blood is rather hard to get with this build
-Low AP makes single shots rather weak

As is normal with Karthus, Defile is a quick and rather easy way to farm creeps for money. What is not usually known is that, when given Spell Vamp, this ability can allow Karthus to solo the Dragon at as low a level as 12. While keeping the ability active, use Lay Waste to do massive damage while regaining the life lost by the Dragon's attacks. When Karthus' mana begins to run low, use Clarity and continue fighting. This will aid not only the player using Karthus, but the entire team.

The skills were chosen the way they were early game for the simple fact that Lay Waste is powerful enough to remove large chunks of the enemy life bars, while Wall of Pain simply slows enemies down. For a build relying more heavily on large numbers of early creep kills, consider swapping the Lay Waste and Defile build times, though this will make extended fights harder in the early parts of the game.