I remember making a thread like this last year, and this board can always use a little bit of discussion.
2013 was a pretty big year for games, even if you take away the releases of the Xbox One and PS4. Bioshock Infinite, no pun intended, shocked everybody, The Walking Dead returned and allowed us to play as Clementine, The Last of Us made every 360 owner wish they had a PS3 instead, while GTA V ended the last generation with a bang and ruined any chance these other games had to win any Game of the Year awards.
So, in short, what was your game of the year? I think I'll have to go with GTA V here. An incredible story, fun gameplay, and everything else you would expect from a GTA game. Sure, GTA online had it's flaws and not heists, but that doesn't take away from how amazing the actual game was. It also had Trevor Philips, no other game can say that.