This is probably more of a "not-AAA-game" rather than a straight up indie thread looking at some of the games, but I'll just post instead complaining (I was just making a promise, not complaining, honest).
Quite a few of mine here already, like Limbo, Mark of the Ninja (although published by Microsoft so yeah- OOPS) and the other great Klei game Don't Starve. A really great developer that Klei Entertainment. I think they have a disclaimer on their web page saying something on the lines of please do play our games on youtube and mod them and whatever, we like that stuff.
Spelunky (original freeware version is my cup of tea) is a seriously good game, there's not much it could have done better. It's like Pitfall times 10 000.
Trine and Trine 2 are the most fun you can have with three players, preferably on the same room.
Rocket League is probably the best sports game there is, thanks to being completely physics based.
I just downloaded a demo of Unholy Heights last night, it's a tower defensy 2D management game, where you play the devil who runs a an apartment building he rents for demons. You raise and lower the rents, evict tenants, refurbish the rooms and knock on their doors to get them to fight the good forces come to robyour building.The graphical and musical style reminds me of SNES Sim City, which is excellent. The tenants have personalities, jobs etc and you can get surprisingly attached to them.
Seems quite great so far, but I can already see the final stuff getting really hectic. But you know, I've always wanted to be a cranky devil landlord, so perfect.
I know I'm forgetting something important now, but I'll come back to it.