There are signs when these civilizations come to an end
Since people are stating Skyrim on account of the fact that it was released late last year and it's DLC and updates were mostly this year, I'll go with that one for both console and PC (I sold the former once I found my laptop could play the latter).
If you don't think that counts, then I guess Assassin's Creed III would be the console GOTY for me, even though I found the ending disappointing. I didn't play that many new games this year, to be honest.
Really, I loved the first two Mass Effect games, but I couldn't even get to the apparently terrible endings of Mass Effect 3 because for some reason, the game just felt way too rushed. Gameplay was good, but although the story had some awesome moments (like the giant thresher maw battling a Reaper; I was FLOORED when I saw that), the overall story just wasn't what I wanted it to be. I sold ME3 to get Black 2; that should say everything.
Handheld, as much as I want to say Black 2, Kid Icarus Uprising was one of the most endearing games I've played on handheld in a long time. Some people think it's repetitive, but that didn't really bother me that much. The game was fun as hell and the dialogue was just far, far too endearing to not love. And it was pretty challenging, too.
Like I said, I didn't play too many new games this year. I'm thinking of getting a Gamefly account to correct that for this year.