- Atom Zombie Smasher
- Frozen Synapse
- VVVVVV (one of the best indie games I've played)
- Shadowgrounds (for same-screen cooperative play)
- Shadowgrounds: Survivor (for same-screen cooperative play - but the first was better)
- Trine (same screen cooperative play, for up to three people)
- Battle for Wesnoth (opensource TBS)
Actually, Shadowgrounds and Trine was by the same company, so you might be able to get them bundled together.
I'm not sure if you'd count it indie, but Dungeon Defenders provided some of the most fun (splitscreen coop, but also online play, and also solo play) for any game I've played, and I probably put in over 75 hours on it. Well worth the money, whether you want to play single-player or coop.
- Spy Party is pretty fun, but rather intense.
- Saira was enjoyable while it lasted.
- I also like to play Galcon Fusion from time to time. Everyday Shooter also.
- For a single cooperative playthrough, the free game At a Distance was fun. Only lasted 45 minutes, can only be played once, and must be played cooperative on two separate machines (laptops are fine) in the same room.
Most of these games I picked up on sale. I suggest adding them to your Steam wishlist, and get a few during the next major Steam sale.
I've heard really high praise, from people who's opinions I respect, for Bastion. It's on my 'TODO list' of games to play.
I'm heavily into 'experimental' design games, and cooperative games, so my tastes might differ from yours. If I had to suggest any one single-player game, I'd say VVVVVV. If I had to suggest any cooperative game, I'd say Shadowgrounds. But then I'd also recommend Dungeon Defenders as a follow up to either of those suggestions, whether I'm suggesting single-player or cooperative gaming.
These are all indie or indie-ish games.