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Hi, I'm Kwaggy. I play Cho'Gath. A LOT. He's my main, and makes up about half of my total time playing normals, mostly as a "tank" (why that's in quotes will become readily apparent soon), with easily the highest win rate. I'm here to share my methods with you. I play Cho'Gath as a solo top (or a jungle if my team desperately needs it), and that's what I'm basing all of my choices here on. Let's start by look at Cho's strengths and weaknesses.

Strengths:
-Feast gives you almost all the health you need, so you save money on expensive health items.
-His base damage and ratios are moronically high for a tank.
+(Corollary to the above smile This ridiculous damage output also lets Feast become a "get-the-****-out-of-my-teamfight-button" because anyone that gets hit by it is either already dead, about to die, or absolutely HAS to retreat.
-He has two AoE interrupts on short cooldowns, so he's where channeled ultimates go to die.
-Vorpal Spikes and Feast makes farming super-easy.
-Feast gives you incredible Baron and Dragon security.
-His /joke is the most hilariously awesome thing you can have your champion say if you're in the shot of the nexus exploding. By the way, you can still use emotes as the game ends, if you didn't know that.
-He can fill any role on the team if he wants, and actually does fairly well in all of them. (Support Cho is better than it sounds if you like kill-lanes, but AD Carry Cho is the only Cho build you just plain shouldn't use.)
-He's the only champion that gets physically larger as he progresses, allowing him to just stand on top of a carry and soak targeted skills because they clicked on you instead of a high-value target. Yes, this will happen ALL the time.

Weaknesses:
-Somewhat short range. Rupture is in what I like to call the "farm-from-the-nexus" category of ranged skills, but it's much easier to land at short range, and Feral Scream only works directly in front of you. Feast is melee-range, and Vorpal Spikes is an on-hit effect on a melee champion.
-Because of your short-ish range, you might get poked out of lane early if you miss your Rupture's a lot.
-Low sustain compared to some other champions you'll be competing against.

And let's just get one thing straight. Cho'Gath is NOT a normal tank. Cho'Gath is a tank that does metric ****tons of damage, and should be played like it. The way Cho forces the enemy team to pay attention to him is because they'd be dead otherwise. This build will have some AP in it, but only the tanky AP items. I've done the math. At level 18, with full Feast stacks, you have an effective health of roughly 14,000. That means that, before resistances are calculated, the enemy needs to do 14k damage to you to kill you. That's not just a lot, that's ridiculous. This build works. I use it almost every game.

So, it's guide time! Let's start with the...

Summoner Spells
You have a few options with your SS's.
-Flash
Always. You have NO blinks. You need Flash to compensate, so always have it.
-Ignite
Great if you're kill-lane-support Cho since it mitigates those pesky heals, great in solo top against most of your negative matchups for the same reason. If you're not solo top or kill-lane-support, I wouldn't take it. If you're solo top in a draft game and know for a fact their solo top has no sustain, don't take it. If you're in the mid lane (which builds and basically plays the same as top Cho except your enemy will be a LOT squishier and appreciate that 3-second silence much less), take this.
-Exhaust
Any time you don't need Smite or Ignite, you should take either this or Teleport. (Your preference.) Exhaust lets you force carries out of a fight for a few seconds while you walk up to them so you can get them out of a fight permanently.
-Teleport
SOLO TOP ONLY. If you don't need Ignite, being able to Recall, buy some items, then be back in lane before the enemy has had the chance to cause mischief is nice. It also will sometimes let you join an important teamfight that you would've missed otherwise.
-Smite
If you're jungling, you should have Smite. Period. This is the only time you want Smite, but if I EVER catch you jungling Smite-less, I will end you.
Now then, on to...

Runes & Masteries:
-Attack Speed Marks
At this point, you might be thinking "Wait, what?" Well, here's the thing. Vorpal Spikes does a LOT of damage. It's the largest steroid in the game that doesn't scale on missing health when maxed out, AND that steroid is AoE. Having higher attack speed lets you get in an extra attack or two in a trade, and it lets you get more pokes in with Vorpal before the enemy realizes what's happening.
-Armor per-level Seals
Cho IS a tank. You do NEED defenses. I used to use flat, but it occurred to me that Cho is more of a late-game oriented champion and I'm not afraid to admit it when I know I'm wrong.
-Magic Resistance per-level Glyphs
Same reasoning as the Armor Seals.
-Movement Quintessences
I have gone back to running Movement Quints from flat health, because you'd be amazed at the ridiculous crap you escape that you shouldn't early game with them. Basically, any enemy jungler with a targeted gap-closer is going to be tearing their hair out because they are just the tiniest bit slower than you are and can't use it.

So there's your Runes, now it's time for Masteries. Your options are either 9/21/0 or 0/21/9. Both have merit, and I flip flop between them a lot. I usually don't see a substantial difference in performance between one or the other. Since either way. it's 21 points in Defense, let's start by taking a look at that.
Resistance: 3/3
Pretty self-explanatory why you'd want this as a tank.
Hardiness: 3/3
Same with Resistance.
Durability: 4/4
Health is good. It makes you be not dead.
Veteran's Scars: 1/1
Mmmmmmm more yummy health.
Indomitable: 2/2
2 less damage on every single thing that hits you sounds pretty neat. I mean, it's not GREAT, but I like it the best of the options available this far up the tree.
Initiator: 3/3
This mastery is incredible. 3% more MS pretty much at every point where I'd really need it? Yes, please!
Enlightement: 1/3
Two points in Mercenary and this point used to be taken up by three in Honor Guard. It seems GREAT in theory for a tank. Turns out, it's not. Do the math real quick. 1.5% reduction means that, per HUNDRED damage you take, you remove 1.5 of it. A particularly large singular hit is around 600-800, which late game isn't uncommon to see. That'd be removing 9-12 damage from those big hits. Thus, it's worthless. A legitimate amount of gold per kill/assist and some extra CDR is much better, as it turns out. If you really want, you can swap this for siege Commander, but that actually sucks worse, because 10 armor is a drop in the bucket for a turret, and you already push like a mofo anyway.
Mercenary: 3/3
24 gold per assist is neat, and is definitely better than any of the other junk you have left to choose from, unless you're jungling. If you're jungling, take the points from this and Tough Skin + Bladed Armor.
Juggernaut: 1/1
This mastery does pretty much everything you like as Cho'Gath. It gives you health you don't need to pay gold for, and it gives you some much needed bonus CC reduction.

Now then, your options in the other two trees like this:
Offence
Mental Force: 4/4
Cho has good ratios, and there's nothing else at the tier you want.
Sorcery: 4/4
4% CDR this low in a tree is sweet.
Arcane Knowledge: 1/1
10% MPen makes you use your ridiculous damage to better effect.

Utility
Summoner's Insight: 1/1
It's more just to use your points than it is because I like the mastery, but you could be doing a lot worse with this since you'll be mastering two spells.
Good Hands: 3/3
Your job description includes "be the first one to die on your team." Being able to do that more often is good.
Swiftness: 4/4
This is almost as good as having Initiator mastery up, better if you tend to get poked a lot.
Runic Affinity: 1/1
Your ult will see to it that you have those fancy buffs on you frequently (can't tell you how often a jungler walks into my lane only to get nom'd because they forgot "oh right, he's CHO'GATH), and if you're jungling you should ALWAYS have this.

So that's masteries. Now, then, it's time for...

Skill Order
Feast>Rupture>Vorpal Spikes at level 2>Feral Scream>Vorpal Spikes
Feast is your ultimate, so it gets priority. Rupture is your highest-damage skill, doesn't increase in cost as you level it, and has the strongest crowd control you offer. Taking a point in Spikes at level 2, then leaving it there until it's your last skill, makes last-hitting really easy. Feral Scream does a lot of damage, is easy to land, and is an interrupt. However, if you're having trouble last-hitting, you can level Vorpal Spikes instead of Feral Scream. It won't kill your teamfighting too badly, and makes last-hitting easier. Now that that's out of the way, let's move on to...

Item Build
First, look at your opponent's team composition. You should be able to make a guess as to the enemy solo top. If the enemy solo top has lots of skill shots, or some other factor that requires you to dodge things a lot, you want Boots of Speed, and three health potions. If they're not, then grab a Ruby Crystal, since between that and your Runes and Masteries, you start off with a stupid amount of health at level 1.

On your first back, you want to walk back into lane with Boots of Speed and a Catalyst the Protector. This makes your lane sustain ridiculous, and Boots are necessary to not dying.

On your second back, if you make one, finish a Rod of Ages. If possible, finish your Tier 2 boots as well. Mercury Treads if they have a lot of magic damage or CC, Ninja Tabi if they don't have either of those.

Now, look at the enemy team comp, and LOOK CLOSELY AT THEIR ITEMS. If they've got a lot of magic damage, build a Force of Nature, or a Quicksilver Sash if they have a suppress. If they have mostly physical damage, grab a Chain Vest. You'll finish the item it goes into later. (By the way, the item it builds into is why 90% of people I tell this build to think I'm insane, but trust me, it works.) Now, if you already have your FoN/QSS, then start working on a Frozen Heart or a Guardian Angel. Frozen Heart if no one else is building one, GA, if someone is. If you already have that Chain Vest, build a FoN/QSS.

Before you start doing anything else, you should have finished your FoN/QSS AND your FH/GA. At this point, build an Abyssal Scepter. Cho's ratios are too good to waste, the Aura helps your entire team, and the MR is really good to boot. This item is practically made for you.

Now, I mentioned that this next part makes most people think I'm insane. The item I'm talking about? Zhonya's Hourglass. Yes, seriously. It's the only source of both AP and Armor, and you already have enough health that you only care about more resistances and doing more damage. The active is great for those times when you're caught by yourself, as it lets you stall 2 seconds as your team comes to save you. Try not to NEED saving, but sometimes it'll happen. It's also worth noting that you should NEVER, EVER, under ANY circumstances use the active when you're in an actual teamfight. You buy it solely for the stats and not the active ability. If there's more than three legitimate threats alive (which will usually boil down to their AP, their AD, and either their top or jungler), then you shouldn't be using Zhonya's active since it's your job to take their damage. The only time it's acceptable to use it is when you've been caught alone and out of position, AND you have teammates nearby coming to help.

So, that's your item build, and that's my Cho guide. I'll take any questions about strategy situations below.