I'm going to be upfront about this and say that I have played very few games that released in 2013. This has a been a year when I have gone off gaming, for the most part. I think it was E3 that did it, but that's a story for another time. I can't and won't comment on the likes of Bioshock Infinite, The Last of Us, or Rayman Legends and I won't be getting Assassin's Creed IV, Watchdogs, or Super Mario 3D World, so I'll leave those out as well. You might be wondering why I've even bothered posting since I've ignored most of this year's top contenders for Game of the Year awards.
To be brief, E3 showed me why I've stopped caring about video games over the past few years, while Nintendo have been doing everything they can to remind me why I fell in love with them in the first place. I won't bore you with the details but the ending is that, while I know this hasn't got an ice cube's chance in Hell of winning, I personally would give GOTY 2013 to 3DS Streetpass.
I am fully aware that Streetpass itself is not a game, but it was simpler to type that than list all of the actual Streetpass games themselves. Nintendo released four new games for Streetpass earlier this year and they deserve the title, as far as I am concerned. They're all just really fun, for one thing. That's probably the most important part. They also show how Streetpass can be used in different ways, whether it's to save the galaxy from robot pirates, chase ghosts out of a spooky mansion, or simply cultivate a beautiful garden.
Really though, the reason I would give Streetpass the title goes beyond the games themselves. I fell in love with video games as a child because they gave me common ground with other kids and enabled me to make friends. I still remember when Pokémon first came out in the UK and every single child in school became friends through the game. No one was mean to anyone else, no one would stick only with the people they knew; everyone had something in common with everyone else and it brought us closer together. That feeling of community has all but vanished from video games for me. The rise of online multiplayer killed going to a friend's house to play together. Being exposed to aggressive, simple-minded, hate-filled people on the ends of microphones dulled the spark of saving the world. Overly simplistic tutorials and invasive HUDs made me feel like I was being treated as a child with too few brain cells to rub together to make a fire. As my friends grew up, many of them packed away their consoles because they no longer had the time to play as much, what with jobs and University and, in some cases, families. This is why I wouldn't consider GTA V for GOTY; here is this huge, detailed world of fun and possibility, and yet not a single person I want to share it with.
Streetpass has given me that feeling of community back. If you own a 3DS, you are already playing. All you need to do to play is be near another owner. Streetpass has encouraged me to go to specialised 'meet ups' and events in the city (where I even won a Mario Kart trophy in a little tournament). You get to know people, you get to have fun anywhere, and it's so simple that it'd be harder to not get involved. To put it bluntly, it makes walking down the street exciting, and not a single other game I can name has made real life more enjoyable.
That's just me though. Actual publications and awards bodies will go with the likes of Watchdogs (I presume), The Last of Us, or GTA V.
Different places vote different games because there's different merits people look for in a GOTY. Some people look at what is technically the best. Some look at what's innovate. Some look at simply the experience it gave them. And the best places look at all of those things! 
And likewise, The Walking Dead delivered an amazing story but it was hardly the most stimulating gameplay experience. But that was my last year's GOTY by a mile.
