Well, as a European it would be Persona 4 Golden hands down.

But if we're going by US release dates, it's GTAV, with The Last of Us a close 2nd.

Didn't play that many games this year honestly. Still haven't played GTA and Mario 3D world, but from the games I've played TLoU is first and Bioshock Infinite is second.

That would be as absurd as me saying how are people saying Super Mario 3D World. It is essentially 3D sonic with slightly better story, visuals, and better playable characters.

I understand not liking it if you are not a fan of fps or even just not liking the type of game bioshock is. But Bioshock Infinite plays nothing like CoD. 

The reason I loved it was because it gave you a wide variety of combat options with the vigors, guns, and skyhook. It had a creative and interesting story. It had memorable characters and the most interesting setting of any game since the first bioshock. And for the most part it was a blast to play. My only problem with it was that certain portions of the game felt tacked on and the friendly AI never moving or doing anything ruined the immersion. 

Anyway my GOTY would be Luigi's Mansion: Dark Moon. I never played the gamecube version, so the gameplay felt incredibly unique. The bosses were mostly fun and interesting. There was a wide variety of enemies and puzzles. The humor was great. Only problem with the game was that the difficulty curve was all over the place. I remember getting stuck at certain levels for hours and then solving the following levels in minutes.

Honorable mentions.
Grand Theft Auto 5
Bioshock Infinite
The Legend of Zelda: A Link Between Worlds.

I feel the need to make a top 5:
1. Fire Emblem: Awakening
Over 200 hours spent playing this game. It pretty much became GOTY one I realized how flexible the skill system is (unlike other games in the series, which are great but comparatively rigid).
2. Slot reserved for when I finish A Link Between Worlds. ;) It may become #1, but not until repeated playthroughs.
3. The Stanley Parable
A hilarious and thoughtful narrative experiment, made memorable with excellent narration and clever secrets. Mark my words- The Stanley Parable is going down as an indie classic.
4. Batman: Arkham Origins
Screw the critics. I wanted more Batman, and that's exactly what I got.
5. The Wolf Among Us
I've only played the first chapter of TWAU, and I'm already convinced that Telltale has a wonderful adventure game formula on its hands. The great soundtrack and wonderful art style doesn't hurt.

Super Mario 3D world followed closely by Wonderful 101 and Pikmin 3. A big shout also for Lego City Undercover, not quite game of the year material but a very fun experience indeed.

Lot of games I haven't played yet due to business/brokeness. But, so far...

1. Wonderful 101
2. Super Mario 3D World
3. Fire Emblem Awakening
4. Bioshock Infinite
6. Luigi's Mansion
7. Fire Emblem Awakening
8. Pokemon X/Y

Super Mario 3D World and Fire Emblem Awakening, both are incredible games even though I still haven't finished them yet.

The Last of Us was good, but I wouldn't pick it as my GOTY. Still it deserves a mention.

Played through Bioshock Infinite recently and thought it was definitely going to be my GOTY. Played Last of Us right after though.. poor Bioshock didn't stand a chance. From the opening scene right to the last moments. What an experience.

But Bioshock was still awesome.

If I had to do a top 5...

1. Super Mario 3D World
2. Bioshock Infinite
3. The Last of Us
4. Pikmin 3
5. Rayman Legends

I don't even know how many games I've played from 2013. It seems like very few.