I remember three games dominating the discourse of 2013, The Last of Us, Bioshock Infinite and GTA V, I unfortunately haven't played The Last of Us yet, but here is my take on the other two:

GTA V has a terrible story and boring characters, Michael Bay-like missions without any freedom for the player and an open world without any personality, attention to detail or depth in its interaction. Overrated and mediocre. GTA IV is a much better game in my opinion.

Bioshock Infinite is even worse, I legitimately think that is a 3/10 game, a lot of very interesting ideas that are only explored on the surface, they basicly replaced the exploration and immersive sim elements of the first two games with repetive shooting galleries with the most bullet-spongy enemies you can imagine. The multiverse nonsense story is very clumsy handled and feels completely out of place in the Bioshock universe. There so many strange choices in the game design, like why did they design an upgrade system for the weapons, when you can only carry two at a time and you never know in advance which weapons the game will provide you with ammo for? Oops I invested everything in the machinegun, but the game decides I am not supposed to use it for the next hour. Really? The skyline makes the game feel more arcade-like and again less slow and tense (which made the first two Bioshock games unique), combat arenas seldomly seem to be designed around you using the skyline anyway, except for the final boss. The game also gives you the illusion of choice several times and downright treats the player as an idiot on multiple occations: It doesn't trust you to actually aim and throw a ball at a key moment in the story, and who can forget this puzzle:

I wonder what the solution might be.

Anyway, this turned into a rant. There are a lot of great games of 2013:
Papers Please is a brilliant way of merging addictive gameplay with political commentary. It is very well written and a lot of fun to play.
The Stanley Parable is thè meta videogame, super creative and entertaining, I almost decided to vote for this one.
Super Mario 3D World is one of the greatest Mario platformers in my opinion. Top tier level design. Almost voted for this one too.
Pikmin 3 is another one that made the Wii U a great system. Looks gorgeous too.
Rayman Legends was 2D platformer perfection, though I still slightly prefer Origins. Who can forget the great music levels!
Tomb Raider was a brilliant reboot. Maybe too focused on action over puzzles and exploration, but when the action gameplay is that good, I don't really care.
But in the end I voted for Assassin's Creed IV: Black Flag, this game has a brilliant story with great characters and setting, sandbox game design that actually gives you options to complete missions multiple ways and a lot of solid side content.

A really great year.

My pick goes to A Link Between Worlds. I was wary of this sequel to A Link to the Past before it launched, especially because of reused areas. But I was very wrong. It’s one of the best Zelda games ever and my choice for best 3DS game. I love the sense of adventure and discovery; the dungeons, bosses, and puzzles; the subtle 3D effects and remixed music; and, of course, the wall-merging mechanic.

Out of this list, Super Mario 3D World. I was shocked they could make level design that good without the space/gravity gimmick of the Galaxy games. But if Fire Emblem Awakening counted as 2013 for its Western release that would take the cake. The story and gameplay of Awakening gelled in a way I hadn't seen since the original Bioshock.

Fantastic year for gaming, especially after last year. Unfortunately, it all goes downhill from here for the next three years but at least there were a bunch of quality releases in 2013. Among some great games like Pikmin 3, Rayman Legends, Tomb Raider and MGSR, it comes down to four games for me:

Super Mario 3D World was fantastic and a ton of fun, but not quite GOTY. The Last of Us was amazing story telling and a great game, but I still had more fun with something like Uncharted 2 as far as gameplay. Bioshock Infinite would probably be my pick for all that it does right, but sadly, there are just too many things about the game that bug me, like many levels being a bit boring or feeling like a chore to play. But probably the single biggest offender to me was

That said, the best moments with Elizabeth made the game all worth it in the end and it's still leagues better than the cheap, forgettable cash-in that is Bioshock 2.

Therefore, my vote goes to Zelda: A Link Between Worlds.  Nintendo made up for the two cluster f@cks on the DS by not only making the game control, well, normal again, but also being a direct sequel to arguably the best game of all time.

Luigis Mansion for me this year.

My vote goes to The Last of Us here, followed closely The Legend of Heroes: Trails of Cold Steel whose original Japanese release date was in 2013, but there are quite a few other games I enjoyed as well from 2013. Papers, Please, the Tomb Raider reboot, The Stanley Parable, Rogue Legacy, Brothers: A Tale of Two Sons, and Guacamelee! were all great in various ways, just not quite the best of the year.

Dota 2 for me. Think I've played it more than any other game, even StarCraft & Diablo II; it's very addictive. Also props to Valve for making a complete F2P game that had no P2W whatsoever, with all heroes being free to use and only cosmetic items and battle passes being purchasable (and a share of those battle pass proceeds going to the pro scene, which was also fun to follow).

Runner-up is Grand Theft Auto V.

Most disappointing is BioShock Infinite; aside from the setting, almost nothing about that game worked for me, and so much content was clearly cut that the finished product was a shadow of what we saw in those first gameplay trailers. 

There's only one correct choice and it's The Stanley Parable. The employee lounge alone makes Last of Us and GTA V look like amateurs, and don't even get me started on the broom closet!

Anyways my top 5 for the year:

1. The Stanley Parable
2. The Last of Us
3. Metal Gear Rising: Revengeance
4. BioShock Infinite
5. Grand Theft Auto V

A decent year, with some good highs, but like last year most credit goes to the 3DS because most of the console games I played wouldn't go very far. Of the poll I played Tomb Raider, The Last of Us, Zelda A Link Between Worlds and Super Mario 3D World. Of the 'other' list I played Batman Arkham Origins and Luigi's Mansion 2 (or 'Dark Moon' as it's called elsewhere).

To get things out of the way; Batman was forgettable, and I really didn't like The Last of Us. I could say a billion things about how terrible it is, but let's just keep it at that I'd say this is easily Naughty Dog's worst effort I ever played, especially with the then still fairly recent Uncharted 2 and 3 in mind. Anyway, luckily those two duds wouldn't overshadow what otherwise was a, like I said, decent year. Not even the release of the final nail in the coffin of SimCity, once one of my favourite series could change that. However that pain was already suffered in 2007, it would make me label EA as 'evil incarnate' forever after, and it was a such a giant flop that it made another company completely and utterly conquer the entire genre two years later. It was laughable really more than frustrating.

But I got sidetracked again. Tomb Raider was a pleasant surprise. I liked this game very much. I thought it was a highlight of the year. It was adventurous, with some good puzzles and action, a cool world, nice story and it actually did collectables right for a change. To compare it to Uncharted, the collectables in Tomb Raider actually make sense, are items that are where you'd expect to find such an item and they provide a wealth of backstory. It made me want to go out of my way to find them. Super Mario 3D World was good, and the cat-powerup is here to stay, but it was obvious that the concept of this game was made for 3DS with 3D Land; 3D Land was better at being a handheld game than 3D World was at being a home console game. Lastly Zelda A Link Between Worlds was a good entry in the Zelda series as well, though it was a little too similar to it's spiritual predecessor A Link to the Past. It made sense in that game that the Dark World was a mirror image of the regular world, but Lorule needn't be like that. I also wasn't much of a fan of the item renting, but the dungeons and the 3D effect were great.

Besides these this year I also played God of War Ascension, which can't stand in the shadow of God of War 3 and Zelda The Wind Waker HD, which was a good remaster that made me look upon this game more favourably. Then I also played Total War Rome 2. This was met with much criticism upon release, but I thought it was great. The campaign map is the best in the series and it makes for countless hours of playtime and I still play this every once in a while to this day. Admittedly, it did need a lot of patches to get the game to what it is now, today. I might have forgotten how it actually was back when it released.

Lastly I didn't mention Luigi's Mansion 2 yet, and that's because that game was the absolute highest highlight this year. Again the 3DS's 3D effect was put to great use, and I'd say the greatest use, because every room and location looked like an interactive diorama because of it. I loved how in this game there were more 'mansions' than one, each with their own theme. All the while the game doesn't overstay it's welcome. If you can critique it, you could say the game's ghosts don't have the character of those in the original and of the sequel. However that is minor. This year is between Luigi's Mansion 2 and Rome 2, but because Rome 2 took a while to get to what it is today, Luigi's Mansion 2 (other) wins.

A stacked year!

I played and enjoyed Bioshock Infinite, Tomb Raider, The Last of Us, A Link Between Worlds, Super Mario 3D World and DmC: Devil May Cry. If I had to choose a winner from the lot, it would be A Link Between Worlds.

2D Zelda games are so rare nowadays and even though they reused A Link to the Past's map, this game felt brand new. Loved searching for octopus babies, exploring the multiple dungeons and the "wallpaper" power was inventive and a lot of fun.