GOTY: Portal 2. It's very close to being my favourite game ever made.
Other than Portal 2, it was still an awesome gaming year, perhaps the best ever. Any of my other candidates could win most other years: Deus Ex: HR, Skyrim, Arkham City, Battlefield 3. Add to that some great games like (and some might argue some of these) Rage, Crysis 2, Shogun 2, Dead Island, L.A. Noire, Saints Row The Third and a handful of indies like Trine 2, The Binding of Isaac, Terraria, Minecraft, Orcs Must Die, Bastion, From Dust, Dungeon Defenders and as I said, it's probably the best gaming year I've seen.
I generally don't buy crappy games and I don't understand people who do so I prefer calling the worst game of the year the most disappointing game of the year and this year there's only one answer: Dragon Age 2. I tried to be prepared for it after seeing the trailers and the direction they were heading but I still wasn't ready for the ungodly amount of recycled content and enemies spawning out of thin air. The game had few good things going for it but there's no way around it, it's a huge disappointment and probably ruined the franchise already.