Valdis Story: Abyssal City. Single best game I played in 2013 (independent or AAA), nothing really came close. Trailer doesn't really do it justice, as it fails to show off the puzzle, exploration, diverse gameplay styles, and not to mention epic boss fights and one hell of a soundtrack.
https://www.youtube.com/watch?v=MK0wkXNcuK4
Freedom Planet. Another awesome one, also a 2D game. These out Sonic'd Sonic with this one, as it really could serve as a proper successor to Sonic 3 & Knuckles, which was the series' highpoint immediately after Sonic CD. It's very much what you would expect if Sega Technical Institute and Treasure got together in the early 90s to develop something for what would be the next generation's (back then) Sega Saturn. Varied and creative levels, excellent gameplay, awesome bossfights, very pretty sprite work, and once again an amazing soundtrack.
https://www.youtube.com/watch?v=fjU8RFso8jI
Bastion. Almost an indie game, Warner Bros. did get to slap their logo on it (they didn't get to do that with Transistor though) though, they had no creative freedom with it. My pick for game of the year in 2011, to me it was better than The Witcher 2, Deus Ex 3, and EYE Divine Cybermancy.
https://www.youtube.com/watch?v=VZAuKkv4eZE
EYE: Divine Cybermancy. This made Deus Ex 3 look bad in my opinion and that is saying a lot. In spite translation problems (lol they google-translated it from French, a fan patch exists to properly translate it to English), it was the single best first person game in my opinion to come out of 2011 and by far one of the deepest games I have EVER played.
https://www.youtube.com/watch?v=DO3b0u6dovk
Pier Solar. This one was actually a kickstarter project originally for the SEGA GENESIS AND SEGA CD, though it recently got ported to Dreamcast, Windows, Linux, and I believe Mac OS X. I actually have the Genesis version along with the Sega CD-compatible soundtrack (you can use the CD music if you have a Sega CD). Pretty good Japanese-style RPG.
https://www.youtube.com/watch?v=fUg-tD2M8jo
ECKZBAWKZ HUGE LIST OF ACHIEVEMENTS GOES HERE....
Oh wait.