There are so many I want to recommend.
Super Meat Boy is one of the best platformers I've ever played. It's ridiculously simple, but the design is excellent. It teaches you and it punishes you, so you learn to do nearly impossible things.
Uplink was one of the first indie games I played. It's a real testament to what you can do with incredibly few means. It's about hacking, and it's completely unrealistic and stylized, but it really makes you feel like a sneaky, brilliant bastard.
Flotilla is an acquired taste, mixing the turnbased/realtime-resolution mechanic of Combat Mission with the 360 degree space combat of Homeworld, in a completely whacky randomly generated campaign. I can easily see most of the world hating it, but I've had great fun with it.
FTL probably doesn't need an introduction, but like Uplink it's a great example of what you can do with some very limited elements. Create a bunch of systems, implement them into a spaceship, and send it through space. I wish it was longer and more varied, but it's still a total gem.
My newest darling is Escape Goat, and it kinda blows me away because there's literally nothing about the game that is special at all. It's a bog standard platformer, but it just fucks with the level design in the most delightful way.
In general I'll check out anything that has Introversion, Blendo or Team Meat stamped on it. Hasn't failed me yet.