Hello!
This guide is a fun, yet viable and simple build that I've been playing around with for a while now. I frequently go into different "moods" when I'm playing LoL. Sometimes I feel like playing an AD champion, or maybe an AP champion. However, when I feel like being greedy, I use this build. Hence the name :) Enjoy.

The entire foundation of this build is first Greater Quintessence of Gold. Along with one mastery point into Greed, along with the GP10 items you buy early in the game, you'll be pleasantly surprised at your income whenever you look at your gold pool.

Marks:
Greater Mark of Magic Penetration x 9
Seals:
Greater Seal of Replenishment x 8
Greater Seal of Evasion x 1
Glyphs:
Greater Glyph of Magic Resist x 9

Magic Penetration marks are also essential for such a strong dps caster; that much is obvious.

For Seals, I prefer flat Greater Seal of Replenishment over Greater Seal of Scaling Mana Regeneration for the sustainability early game, as you will have little to no mana problems late game anyway, as long as you play smart. I also keep that single dodge seal for that once-in-a-great-while dodge that happens. Sometimes its inconsequential, and sometimes it prevents your enemy from getting that last hit on you when you're at 10hp, allowing you to say "/all LOLNOWAI."
All I know is: .75% is infinitely greater than 0%

"Smite? Wait, when did this become a jungle guide?" Don't worry, it's not. Just hear me out! You may be thinking that I chose smite and its mastery for the extra 5 gold, but its not. (although the extra pocket change isn't bad) Smite allows me to steal the enemy big-wraith at level 1, both giving me a level advantage in mid, and giving the enemy jungler a small disadvantage. Either that, or I can leash my teammate's blue using smite, giving him a lot of help in jungle. On top of that, you've got early dragons, and easily stolen buffs that your enemy simply doesn't expect from having an extra smite on your team. I've personally grown to love smite, and I do believe it to be a significant part of my build. (Just don't steal your own jungler's monsters)


My personal pick for Karth's utility spell. IMO, He's very damage oriented with little defensive capability, so most would agree that Flash is the most useful spell for him. Not only that, but because of his passive Death Defied, it's sometimes best for your team to suicide in a strategic position. And where better to leave your AoE ability than in the middle of the enemy team?


My second-favorite spell for Karthus. If it weren't for the usefulness of Smite, then it would be my #1. Clarity allows for an INCREDIBLE amount of spam capability early game, allowing Karthus to be almost 100% mana sustainable at level 1. With Clarity, you can both last-hit and harass the enemy without EVER running out of mana between its cooldown (with smart use of your abilities, of course)

For masteries, like in most Karthus builds, I go 9/0/21. Feel free to nitpick to your choosing, but here are my thoughts on a few masteries.

Greed is important to this build. By itself, if you actually do the math, its use is pretty underwhelming. But since this guide centers around the collection of gold, its usefulness is just a little extra gravy to the build. This mastery point is just like having an extra Quint slot!

I implore you, if you try this build, try it with Smite + Plentiful Bounty at least once. The extra gold, and wraith/jungle steals are very satisfying and consistent.

For this build, you must go mid. If you're playing Karth, your team will probably let you go mid anyway, because honestly, he is probably the best solo laner in the entire game. (Although that's entirely and completely my own opinion)

I start off at the enemy wraiths, making sure to carefully and slowly check bushes for enemies protecting their jungle. When you see minions making their way down, start floating to the wraiths and Smite the big one, and head to mid. Congratulations you just annoyed your enemy, gained half a level and 40 gold for free.

Spam the hell out of smite whenever the opportunity arises for that little extra gold boost, because the cooldown is so short, you don't want to waste any time between its uses. If you don't have a jungler (which you should), feel free to jump out of lane for a second to clear your own (or enemy's) wraiths. Don't go straight through mid though, or you will be easily ganked.

You will notice that my starting items don't use all of your starting gold before you jump into lane. That's because you want to get your Philosopher's Stone A.S.A.P. As soon as you have enough gold to buy it, push your lane hard. I know leaving your lane is bad, especially when you don't need to heal/get mana, but getting your GP10 items asap is essential. Run back down to mid, and if you pushed at the right time, your enemy shouldn't even have gotten a single attack on your tower by the time you're back.

Rinse and repeat until you have Heart of Gold.

This is basically the infrastructure to the entire build. After boots I either go for a Rod of Ages or Archangel's Staff, and building them depending on whether or not I feel I need the survivability or AP more.

Kage's Lucky Pick
You may be thinking: "If you're focusing on a GP10 build, why didn't you include Kage's Lucky Pick?" Well there's a couple of reasons. For one thing, I don't believe it's as useful as the regen bonuses of a Philosopher's stone and the great early health bonus of a Heart of Gold. 25AP simply isn't enough for me to want it. Not only that, but if you had Kage's pick along with the Philo stone and HoG, there simply wouldn't be enough room. When building all the items for an archangels staff or a rabadon's after you already have your first couple of items, you plainly and simply wouldn't be able to fit the smaller parts into your inventory, making that Kage's lucky pick look mighty unfriendly when you have a Blasting Wand but no room for your Needlessly Large Rod. By the time you sell it, you probably wouldn't have gained enough money to make a profit anyway.

After you get your Rabadon's Deathcap, proceed with the build as you see fit. Here are a few suggestions:


Nice AP and some Nice armor are nice, and the the item's active is useful as we all know. But what makes this item great for Karthus is that his Defile continues even while he is in the stasis. So if you're a glass cannon fighting other glass cannons, this item can guarantee you 2 seconds of nonstop dps, as well as disorienting the enemy in a team fight.


How's about ANOTHER Archangels? You can never have enough! AP is delicious for Karthus!
My very LATE-late-laaatte game consists of
Archangel's Staff x 4
Rabadon's Deathcap x 1
Void Staff x 1
This is basically the Pure Dps build; But other items may be better depending on the situation


A very fun item to get on Karthus. Having this item means popping your Defile forces your enemy to fight because they'll never escape your whirlpool of death :>
But that's only one of its uses. If your teammates are chasing an enemy who is bound to get away (A low singed, or a nidalee) on the other side of the map, just pop your ult, and you'll apply the slow from Rylai's onto every enemy on the map :)


Also another fun item on Karthus. If you use this to compliment your late-game build, your Defile basically makes you Mordekaiser and makes soloing baron a breeze. However, the item is very expensive, so I'd suggest only getting it if you're not too far behind.


This item is a matter of taste; It works very well early game, but starts to drop off late game. Before your jungler jumps into a gank, start channeling your spell. That way your gank turns into a 4v2 at rather than a 3v2, and you get a free stack for your assist(s). Do this every chance you guys get, and you'll be racking up stacks. However the reason I don't like getting this item on Karthus is because
1)It's dependent on having a good team, which isn't really in the spirit of this build :)
2)When team fights start happening, Karthus dies a lot. Both because his passive makes it advantageous to die, and because he'll be focused first. Even in games where my team was doing well, I found myself floating around the 10 stack area.

Skill sequence is the same as any other Karthus build.
R > Q > E > W
Except I like to get my W at level 4 just so I have that slow available to me whenever I need it

Pros
-Cheap build; The Avarice Quints are just a little over 500 IP!
-VERY consistent; If your team is bad and never sets you up for any assists/kills with your ult, you won't suffer as much because you have a very nice alternate source of gold
-Hard to explain but, to me, it just feels solid. Regardless of if the game is going well or going bad, whenever I look at my gold count, I always have more than I expected.
-It's fun!

Cons
-Dropping Magic-Pen quints for the GP10 Quints drops your damage a tiny bit
-Not many people are keen to the idea of picking up smite if they're not exclusively a jungler
-Getting your GP10 items before your other items may lead to a weak ult at level 6

Well, thanks for reading my guide!
I hope you take the the time to try it sometime. I've found that its extremely reliable and solid, and you don't actually lose much Magic Pen from switching your Quints! If you try it, leave a comment on how you felt about it- it won't let you down! And hell, if it doesn't work out, you can use the Quints for some support builds :)

Happy Karthing and Good luck!