Really hard question cuz there wasn't THE big game for me.
I was pleasantly surprised by Assassin's Creed Black Flag but it sure isn't the best one, I guess.
Funny enough, I have to say Saints Row 4

Although I didn't play it in 2013 but it's a 2013 game. I have a hard time remembering a game that I actually played as much in such a short time simply cuz it is just overall great. I've done like 75% main story now and never was I bored, never did I curse any mechanic - it's just a really good game with a huge amount of fun.
So, yeah... there you go: my best game 2013 is Saints Row 4!
