Cave Story is probably my favorite indie game. I also like Amnesia: The Dark Descent, Terraria, VVVVVV, and almost anything put out by thatgamecompany. Minecraft is cool too (but it's overrated).
Off the top of my head... LIMBO, Super Meat Boy and Terraria. I haven't played Terreria in a long time, but I really enjoyed it when I did my first play through.
@butterbean21 Unfortunately only available for PC a great game however with one of the best stories ive ever seen in a videogame.
I have Super Meat Boy and Braid, but I have yet to really play them. Got both of them from Humble Indie Bundles. Want to play Limbo, just haven't bought it yet for whatever reason.
Totally forgot about Machinarium! That's one of my favorite indie games- probably tied with Cave Story as my favorite.
Minecraft if it's still considered an Indie game, and Terraria but they discontinued Terraria for stupid reasons. "Sorry I'm having a baby, I can't work for another year or so, so I'm gettin' rid of the game." Last time I checked my Science teacher was only out for about 5 days because his wife gave birth.
What's wrong with that? He wants to take care of his baby, so what? Last time I checked, he is the dev so he can do whatever hell he wants with the game.