EDITS AND UPDATES!
12/21/11 - corrected some spelling and grammar errors.
12/22/11 - added pictures and color and furthermore corrected guide which seemed to be out of
place.
12/23/11 - further edited the guide for convenience.
1/13/12 - checked up on every champions stats and updated some minor things accordingly.
Pros / Cons
Cho'Gath is a worthy adversary to any champion. he is fast, deadly, and FREAKIN HUGE! if you have ever played Cho'gath, you were probably following some of the other guides on moba, trying to build tanky. well i will tell you the pros/cons of a AP vs tank cho, then what the pros and cons are for an AP cho in general.
AP VS TANK CHO PROS/CONS
-AP
- very high damage output
- a squishy tank
- can solo most any champion
- targeted first
-TANK
- not as high damage output
- a durable fighter
- needs a team to do any real damage
- tends to be avoided because he's a tank
AP CHO PROS/CONS
-PROS
- damage that only the void can dish out
- godly farmer
- extremely fun to play
- intimidation is his biggest weapon
-CONS
- if skills on cooldown, seems to be decently vulnerable
- overconfidence kills you
- can be focused heavily by a good enemy team
- if feast stacks are dropped, he is targeted much more often
Items
i have strictly AP items, no 
Banshee's Veil or 
Archangel's Staff. with the blue buff , you will have way more than enough mana regen. i take the 
Doran's Ring for early game AP, a boost to your health to be able to survive harassment, and some mana regen to keep you in lane just "that" much longer.
I grab boots of speed and quickly upgrade it to 
Sorcerer's Shoes for the magic pen and speed that it gives. the magic pen for more damage, and the speed for more maneuverability.
Rabadon's Deathcap is an obvious grab. its the butter for you bread, but not the bread. (ill explain in a minute) it gives you that huge boost to your AP which you will need if you want to cause some hell with your 
Rupture, 
Feral Scream, and regular attacks.
I quickly grab 
Void Staff for the magic pen which really helps out for those annoying tanks. magic pen = more damage for later game. if they get magic resist soon, it will do nothing, enough said.
Up next is the bread for your butter, the Lich's Bane. if you are truely looking to cause heavy damage, then i dont know what item is better to grab than it. this item gains more and more AP damage every item you get, not to mention the 30% boost through the rabadons makes it the hellbringer for your favorite gentleman. in the end game, you will have some high AP, so this item will be the damage dealer for you and will save you from more than 1 squishy occasion. i cannot stress the importance of this item and recommend it ASAP. YOU CAN NOT DO ANY SIGNIFICANT DAMAGE WITHOUT THIS ITEM!!!
Soon after Lich's Bane, grab Rylia's Crystal Scepter. with Ruptures slow and Rylia's slow, an enemy cant escape. not to mention, due to your 
Vorpal Spikes, your regular attacks will slow down any enemy trying to escape. an added bonus would be the hp which would make you that much harder to kill.
as my final item, i grab 
Zhonya's Hourglass. this item has the beautiful feature of taking all the damage for you and you coming out unscathed. i normally use this item to engage team fights, as strange as that may sound. i rush into an enemy team (but never without a team of my own to back me up in these scenarios) and as soon as i notice that they have started targeting me, i pop Zhonya's Hourglass to take all their spells for 2 seconds, which for some reason they just keep casting. also a great skill if your under a turrent and an enemy is chasing you with low hp. a very useful item indeed.
Farming
because of your jesus like Vorpal Spikes, you can fight off huge minion waves in seconds. combined with Rupture and Feral Scream no minion will be left alive.
for early game farming, obvious thing to do is last hit minions. due to the Vorpal Spikes, you can do more than usual damage to single enemy minions and hold back any melee champs that would attempt to harass you with a regular attack or two. later in levels you can mow down enemy minions and run right through nuetral monsters such as the blue golem, red lizard, and dragon because of the unnatural spikes that come out of your chest with your bidding. if you would like to, grab an extra Doran's Ring or two after your 
Boots of Speed if you would like to harrass just a little bit more. one thing i would like mention is that your passive gives you mp and hp everytime you kill ANYTHING. keep it in mind so you can harass with the mana boost and stay alive with the health boost. once you master the technique of using your Vorpal Spikes to kill minion waves for mana, you wont need to grab that extra Doran's Ring for mana regen.
a nice little trick that can help you get money, but if done stupidly can get you killed, is farming near a turret. well, not exactly near a turret, more like on a turret. when you push a lane to the point where you are damaging the turret and a new wave of minions have arrived, this is your time to shine. lets say your on the blue team and on the top lane. you are now attacking the turret. stand on the upper left part of the turret so that you are facing the minions wave. this will cause your Vorpal Spikes to damage the minions and help your minions to push the turret and possibly get you some extra cash. IMPORTANT! when near an enemy turret and enemy champions are present, TURN VORPAL SPIKES OFF! if you hit an enemy with them the turret will auto target you, and since you are right next to the turret, good luck getting away with over half health.
Team Work
step 1, DONT DITCH YOUR TEAM! one thing cho excels at is keeping enemies busy, if your team is low on hp and they wont be able to get away, prevent an ace by running into the enemy and silencing feasting and rupturing away. give them time to escape. take one for the team.
step 2, refer to step one
step 3, engeage the fights. Cho'gath has the extremely good ability to not only engage team
fights, but to split up the enemy. how do you do this? well im very glad you asked.
first, see if you can engage from a brush or behind. this is absolutly vital. this will
give your Rupture a huge surprise attack on an unexpecting enemy.
secondly, spread out the enemy team so it will be easy to pick them off. how to do this
is simple. your Rupture should make them spread apart slightly due to the fact that
nobody want to get hit by a knock up and slow. right afterwards, run into maybe 2-3
enemies then use Feral Scream, if your 
Feast is maxed then they should run
because of his intimidation.
step 4, you excel in 1v1 but do not let it get to your head. if you are 1v2 a lane do not be afraid to call for ganks or assists. your team, if they arnt complete noobs, should come to your aid when you ask. you can chase enemies extremely well. you are the fight initiator. so do your job.
step 5, refer to step 2
Creeping / Jungling
i was never a good jungler so i will not even go over this area. sorry
Summary
in closing, Cho'gath is one if the most fun character you'll ever play. well at least for me. i hope you guys have as much fun as i do playing cho, the worlds most loved voidling. have fun and go NOM NOM NOM some squishys!!!!!!!! XD
Build Guide
Discussion (24)
Greater Mark of Insight for the magic pen, which you will need ALOT more than armor pen because... well... your AP cho, not boring old tanky cho. the magic pen gives you a strong advantage in the starting game bush rushes that we all know of. rupture does the damage, enemy burns flash you run away.
Greater Seal of Resilience for more durability in lane. this is especially important of you are solo laning due to the fact that harassment will be strongly focused on you. more durability = surviving minion aggro and regular attacks.
Greater Glyph of Force. the AP per level will help you deal extra damage per level and not to mention will help you stay in lane without having to return for items as often. more power, more kills, more items, more feed, win.
Greater Quintessence of Potency. this will give you a very strong early game advantage with that harass. more AP is just better. you got your over level quints but you need some early game burst.
Summoner's Wrath,
Teleport, 
Surge, 
Ignite, and 
Ghost. anything else to say? naah i dont think so.
