Here are some of my favourites. I'm not a connoisseur of indie games, so I'm likely missing some great ones and my write ups aren't the best, but I didn't want to just dump a load of names. One of the great ones I'm probably missing, is The Stanley Parable, which I've only just purchased.
Dustforce
If you like beating your own records, check this one. It's a platformer, with an emphasis on momentum and learning the subtleties of the game. It also has probably one of my favourite game soundtracks ever, which I listen to all the time. I really love this game.
Rogue Legacy
A "Rogue Light" according to developers. It's an addictive game, which leaves you always wanting to go one more life and it has a good sense of humour.
They Bleed Pixels
An often overlooked platformer, with a nice style, fantastic music and some interesting mechanics. It's hard as hell, but it's really good.
Lone Survivor
A great Silent Hill game, which does a great deal, with very little. If you have any interest in Survival Horror, I couldn't recommend it any more and it was recently upgraded to the Director's Cut.
FTL
There's no shortage of people ready to explain why this one's so good. I'll just say it's addictive, the music is godly, it'll make you feel like the captain of a space ship and it's addictive as hell.
Hotline Miami
A brutal top down action game, dripping in style, which also requires you to come up with interesting strategies. The music is godly. I've completed it on the PC, PS3 and Vita and it's one of my favourites from last year.
Others
Cave Story+
The Binding of Isaac
Volgarr The Viking
Shatter