Torchlight (diablo inspired RPG), Hard Reset (Fast paced challenging FPS), Minecraft like others have said.
Also if you are wanting to get cheap indie games in bulk I highly recommend Indie Humble Bundle's website and Indie Royale. Can get some good gems for super cheap when packages are rolled out. I can say I have done business with both sites multiple times and have had no problems dealing with them.
minecraft, Cobalt, Super Meat Boy, VVVVVV, Cogs, Jamestown, Nightsky, BIT.TRIP RUNNER, Terraria, Cave Story+, Dwarf Fortress,Super Smash Land, Kerbal Space Program, and Gratuitous Space Battles can be pretty fun.
Those are all the ones I have played that I think are really fun but my Favs are probably,
Cobalt, Minecraft, Super Meat Boy, Cave Story+, and Cogs
when I am in the mood for some puzzles.
I'm a big fan of Frictional Games' survival horror games, Penumbra (Overture and Black Plague / Requiem) and Amnesia (The Dark Descent and the upcoming A Machine For Pigs). Of course, I also love Minecraft, but that game has become so popular that I'd almost hesitate to call it an indie game (though of course Mojang is in fact an independent developer).
The Binding of Isaac - Plain and simple, has HUGE replay value. There aren't many games I play over, and over again such as Binding of Isaac. It's very unique and fun to unlock all the new stuff and see how Isaac changes in each play through (as they are all unique).
Minecraft - This is definitely a given.
Audiosurf - Fun to play here and there.
Terraria - I have not played this *yet*, but the second it's on sale I'm getting it. It looks like tonnes of fun.
Super Meat Boy - Well, it may drive you insane playing it! But it's a blast.
I could go on forever about my favorite indie games, but I'll limit my raving to only the cream of the crop.
Atom Zombie Smasher
Orchestrate rescue and quarantine operations in randomly generated cities. Set your helicopter landing zone and pray to god that as many people as possible make it before the zombies overrun them. Hold back the wandering horde with the help of snipers, roadblocks, mercenaries, artillery, and even a torrent of missiles from space! It's an oddly satisfying experience when you've leveled a city, but still managed so save everyone. $9.99 on Steam.
I'm putting this in my list of top 3 indie games. Bastion has the best storytelling that I've seen in years. You'll want to do everything twice to make sure you didn't miss anything! Along with the epic storytelling, this game has an amazing soundtrack and many vibrant environments. $14.99 on Steam
Basically, it's an action RPG that takes place in a world shattered by The Calamity. PLAY IT! PLAY IT NOW!
A mesmerizing platform puzzler in which you manipulate time to collect puzzle pieces, navigate through the worlds, and even reverse death! Another absolute must-play. $9.99 on Steam.
The Binding of Isaac
Oh, poor Isaac. Lost in the labyrinth of your evil mother's basement, armed with only your never-ending tears to defend yourself against the forgotten horrors of the depths. Unlike Braid, this game is very unforgiving. A single mistake could come back to haunt you in later levels, but it's that level of difficultly which makes it so appealing to veteran gamers. The low price point, combined with the seemingly endless replay value makes this one hell of an awesome game. $4.99 on Steam.
The Misadventures of P.B. Winterbottom
Dark, intriguing, humorous, and just plain delicious. Guide this pie fiend through a nightmarish world in search of his one true love: pie. As the game progresses, things become increasingly strange and disturbing, and you're presented with new time-bending puzzles that will often leave you completely baffled. $4.99 on Steam.
The world that Double Fine has created in this game reminds me of LittleBigPlanet in the sense that everything is made out of small odds-and-ends that somehow actually makes sense. Every puzzle in this game has multiple solutions, and they can all be met by performing the proper action with the proper stacking doll. That's right, Russian stacking dolls. You are the smallest doll of all, able to jump inside a doll one size larger, and then into another doll, and another, and another, until you've jumped inside a massive train conductor doll that's 3 times bigger than you! Consistently cute, and full of delightful potty humor, this game held my interest right to the end. $14.99 on Steam.