OFF, A freeware surreal French adventure/RPG from 2008. It has some incredible characters, an insanely creepy story and an awesome soundtrack. I played it a few months back and it's easily now one of my favorite games of all time.
The Walking Dead was amazing too, I played that in 2013 after waiting for all 5 episodes to be released. Roll on 2015 so I can play Series 2 and The Wolf Among Us in full (and hopefully Kentucky Route Zero...)
Dear Esther, Thomas Was Alone, Hotline Miami, Zeno Clash, Okami HD, One Chance (Flash Game), Little Big Planet 2 and Gemini Rue all get a special mention too.