With the recent changes to Feast, I believe Cho'Gath is now best played as a tank. AP Cho'Gath mid is still plenty viable, but that will be covered in another guide.

Items:
Tank Cho'Gath has incredible item versatility, and can be built to the needs of a situation.
Starting Items:
Corrupting Potion is the safes starting item, and helps with early trades, particularly with other melee champions.
Dark Seal is a greedy opening, but can pay off if you believe you can stack it.
Doran's Ring is another decent starting item, particularly if you don't take Teleport, and max Feral Scream first.
Doran's Shield is a good opening item vs ranged harass. Combined with Carnivore and an early Ninja Tabi, allows you to largely ignore ranged harass in lane.
First Item Options:
Sunfire Aegis: great vs AD and melee champions. Helps control lane.
Rod of Ages: gives a solid mix of health, sustain, and damage. Great item for bullying lane.
Everfrost: Serves the same purpose as Rod of Ages, but provides slightly fewer stats compared to a fully stacked rod. It does, however, provide more up-front burst, and setup for Rupture.
Spirit Visage: helps with surviving difficult mage lanes. Provides additional sustain.
Boot Options:
Ninja Tabi: The best defensive boots right now.
Ionian Boots of Lucidity: Great for early caster pressure, if maxing Feral Scream first.
Mercury's Treads: Defensive boots vs heavy CC.
Damage Items:
Iceborn Gauntlet is great for setting up slows for Rupture and providing CDR.
Wit's End: if you're going to get a DPS item, this is the one.
Titanic Hydra: Kind of an awkward item to build on Cho'Gath, but can help with bursting targets, and provides more AoE in fights.
Hextech Rocketbelt: Mostly useful for the gap closer for Feast kills. Not necessary if you can consistently land [Rupture]], but not a bad option.
Liandry's Torment: Provides the most bang for your buck, as far as a single damage item is concerned.
Rylai's Crystal Scepter: A decent mid-game item for helping with locking down targets.
Defensive Items:
Dead Man's Plate: Great armor item for helping you catch people. Excellent mid-game.
Randuin's Omen: Build this if you're dealing with high-crit teams.
Warmog's Armor: Good for the CDR and the heal. Excellent if snowballing. Allows you to split push forever. The health also boosts your burst damage via Feast.
Frozen Heart: Good armor item if your team needs the attack speed slow. Substitute for Iceborn Gauntlet.
Thornmail: Good vs auto-attack heavy teams. Exceptional, as Cho'Gath has quite a bit of natural health already.
Guardian Angel: Great 6th item for game-winning pushes.
Locket of the Iron Solari: Great supportive item if your team is struggling against AoE damage, particularly if you need more magic resist.
Banner of Command: A decent option if you need more CDR. Allows you to proxy push a lane while grouped with your team.
Zz'Rot Portal: Helps split-push, siege, and prevent siege. Supportive item, but not a bad option if you need resists still.