I think the only significant games from 2013 itself that I've played were Bioshock Infinite and Surgeon Simulator 2013. I loved both of them, but there are so many more games from this year that I want to play.
As far as stuff from other years, that I happened to play/finish this year, is concerned, there are some things:
Some games I beat this year that I really like include
Fallout: New Vegas - I first started this in mid-2012, but at the time I had just recently played the previous few Fallout games, almost one after the other (Fallout, then Fallout 3, then Fallout 2), so I was perhaps a little burnt out on the series, which led me to stop playing it in the middle. I got back into it this year, and continued on through to the end. As a fan of the previous Fallout games, I really enjoyed how this tied into the others, and the places (both story and location-wise) that this takes the series in. I also really enjoyed some of the DLC a lot; Dead Money in particular was great. I found Old World Blues underwhelming though, despite it being generally considered the best of the lot. Gameplay-wise it was fine, but I really didn't like a lot of the writing. I don't mind silly stuff, but the sort of silly that was presented in this DLC felt very forced and rather cringeworthy, for the most part. Despite that shortcoming though, I think Fallout: New Vegas is wonderful, and can't wait for Obsidian to make a new Fallout game.
Saints Row 2 - I also played the first Saints Row this year, which I thought was alright. It's really not that remarkable a game though; I found it more fun than GTA, but then I'm not into GTA, so that isn't saying a whole lot. Saints Row 2 however, I felt greatly improved on the shortcomings of the first game, while making the stuff that worked the first time around even more entertaining. I really loved the game's sense of humor, and how it was able to take that humor and mix in some more serious moments, without either side feeling out of place. I've heard the series takes a very different direction with The Third and IV, so I'll have to see how I feel about those games when I get around to them. On its own though, I'm at least happy for Saints Row 2's existence.
X-COM: Terror From The Deep - I love X-COM: UFO Defense, so of course I'd enjoy playing what's essentially more of the game
I liked getting to see new level designs and enemies in Terror From The Deep, and the introduction of melee weapons (and being able to open doors without walking through them!) I thought was pretty neat. This is probably not the best direct sequel that could have been made, but for the sake of being able to enjoy more X-COM, I loved it.
Red Dead Redemption - I first tried this in 2012 as well, and at the time I really didn't like it. I maintain that RDR's in-game tutorials are shitty and poorly implemented; I had to go online to read about how various mechanics and minigames worked. Once I got over them and was able to get into the game proper, however, I began to enjoy it. The story took a bit of time to grow on me, but by the end I was pretty engaged. I fortunately was able to avoid spoilers of it, which in retrospect I'm very happy for. I still have to go back and play Undead Nightmare, but the main Red Dead Redemption campaign, at least, I thought was pretty interesting.
Resident Evil: Revelations - I was somewhat hesitant to play this, since I hated Resident Evil 5 (and didn't bother with 6), but I ended up really liking this. It's not without its faults; most of them originating from 5 (such as the incessant need to have an AI-controlled partner with the player at all times, or the incredibly convoluted bullshit storyline that takes itself way too seriously), but they didn't ruin the game for me. This managed to have the scariest feel I've seen from a Resident Evil game in a long time, and I thought they did a good job of mixing the over-the-shoulder viewpoint with gameplay more inspired by the classic Resident Evil titles. I didn't like how the game kept on switching focus from Jill over to other random characters and their stupid bullshit, which I felt messed with both the overall pacing and the horror feel, but the points which focused on the main story thread specifically were good. It somewhat gives me hope that Capcom might someday make another good Resident Evil game again.
XCOM: Enemy Unknown - I started this in 2012, but it took me until 2013 to beat it; in part because of its extreme difficulty (I played on Classic), and because I decided to go back and finish up Terror From The Deep before making more progress in Enemy Unknown. Which I did, so I eventually beat Enemy Unknown
This is very different from the classic games, so I don't love it in quite the same way, but it's still a very good game that satisfies my taste for turn-based tactics. I have yet to play Enemy Within, but I hope to do so ASAP.
WarioWare, Inc.: Mega MicroGames! - I'd previously played WarioWare: Smooth Moves for the Wii (which I literally beat in a day, but had a ton of fun with), so it was nice to experience the beginnings of the series. I like WarioWare's approach to game design a lot; it's incredibly easy to pick up and play, and it works well as a handheld game.
New Super Mario Bros. Wii - I completed this just the other day, and I really liked it. It's a better multiplayer game than it is a single-player game, but even as a single-player game it's very above-average. I'm happy to have played it, and I'm happy to have a multiplayer game around that I actually would go out of my way to play
Might & Magic: Clash of Heroes - I haven't beaten this yet, but I expect to finish it within the next day or two. It's a very unique mix of RPG, puzzle, and turn-based tactics, which I find incredibly enjoyable. This is the kind of game that I can spend hour after hour playing nonstop and not get tired of. It actually sort of got me interested in the Might & Magic series again; I plan on revisiting Heroes of Might and Magic III when I get the chance, and also am looking forward to see how Might & Magic X turns out.
Phantasy Star - I haven't beaten this yet either, and unlike Clash of Heroes, I probably won't be beating this anytime soon. This is a very long, involving game to play through; especially when you're mapping out dungeons on your own! Prior to this I wasn't really a fan of the idea of mapping out games myself on graph paper, but I actually enjoy doing it here. I think it helps that only the dungeons are first-person, so one doesn't need to go through the trouble of mapping out a town just to be able to find a place to rest or to buy food, etc. Maybe once I finally finish this, I'll give some classic WRPGs a try and see how long I can hang with mapping them out
Aside from the mapping though, I think this is a pretty neat classic RPG. I like the mix of sci-fi and fantasy in its setting, although it's remarkable unoriginal at times, heh. I also like how quickly the turn-based battles conclude, though I dislike that you can't target specific enemies when you make an attack. I hope the later Phantasy Star games let one do such a thing.
Things I didn't like this year:
Duke Nukem Forever - I played through this from start to finish, and I have to say, it's not the worst game I've ever played
The first few levels in particular are really shitty, but it fortunately picks up afterward... to an extent. It never becomes very good though, and the writing is consistently terrible throughout. This isn't nostalgia speaking either; I played Duke Nukem 3D for the first time in 2011 and found it pretty entertaining, but Duke Nukem Forever's writing was very painful to sit through. The DLC for the game, The Doctor Who Cloned Me, I thought was pretty decent though. It's still not great, but overally I liked it more than the main game, and it somewhat redeemed certain aspects of the main game's design, I felt.
DLC Quest + whatever its DLC was called - I think I got this in a bundle a long time ago. I decided to play through it after some people on this forum talked about how terrible it was, just to see for myself
I don't think it's that terrible, but it's also not very good as well. I'm glad I didn't pay money for it on its own; it was a very short game (which considering its quality, might be a good thing), and a lot of the humor just wasn't that enjoyable to me.
my computer's graphics card breaking - I hate this so much! My graphics card broke shortly before XCOM: Enemy Within came out, so I haven't been able to play it. I'm especially upset about it, because I really want to play either an FPS or a turn-based stategy game, and almost all the ones I own are for PC, so I haven't been able to play the majority of them for the past couple months. I need a new graphics card!