You will get as many answers as there are players.
My choice:
Platformer (but i didn`t play a lot of platformers to be honest):
Rochard
Cargo Commander (not sure if it`s an Indie game

)
Wooden Sensei
Turn Based Tactical games:
Underrail ALPHA (this is how fallout 3 should have looked and played like imho)
Xenonauts ALPHA (imvho, better then the new Xcom gameplay-wise)
UFO: Alien Invasion (a free game)
Exodus Wars: Fractured Empire ALPHA (early alpha BUT if you overlook poor animations/graphic at this moment this looks like a diamond gem to me)
Frozen Synapse
Adventure:
Bastion
both Torchlights
MagickaTiny and Big: Grandpa's Leftovers (but it gets boring fast, at least for me)
Tower Defense/similar:
Defense Grid
Revenge of the Titans (loved it at first but it got me bored after a few hours)
Space games (various sub-genres):
SPAZFTL
Salvation Prophecy (a real gem, unfortunately not well known. You get RPG elements, TPP space arcade shooting, FPP planetary conquest and strategy in the later game)
MinerWars 2081- i got very dissapointed with this game (there supposed to be an opened world with sandbox elements). This is also the only Indie game i don`t trust the Devs (sometimes it looks like they are just money grabbers)- nevertheless the game is awesome if you like space arcade shooters.
2hard to name a genre:
McDroid BETA(i fell in love with this one, Devs are most community-friendly i have ever seen) - you can call it rts, tower defense, action shooter.... HIGHLY recommended imho
Mobiloid- it`s essentially a 3d platformer where you play as a robot- gather additional parts and then use them to get to previously not accessible parts of the map.
Rawbots ALPHA- just two words (GET IT).. if you like building and programming robots. I wouldn`t even call this piece of gold a game.
Cortex Command- only get it if you like spending alot of time to learn the game mechanic. But you will have HEAPS of fun once/if you do.
I guess there are many more but i`ll stop here

Btw, i have bolded the games on the list i like the most.
Oh, i forgot to mention that some of the games above are actually betas

.