Here's some freeware titles that come to mind:
Knytt and Knytt Stories- Both are atmospheric platformers, featuring some very nice, minimalist graphics. Knytt Stories has a good level-editing community, too, so that's worth checking out.
Hero Core- Made by Daniel Remar, the guy who did Iji, for those not in the know. It's basically a Metroidvania that plays like a shmup, with some really nice chiptune music and extra secrets/game modes. I used to play this game non-stop, it's that addicting.
Deadly Rooms of Death: Architect's Edition- This is the original version of the DRoD game that was released in the Windows 95 era, and is a very unique puzzle game. For those not in the know, it's like Zelda, but it's turn-based. Taking a step or turning your character takes one turn, and every time you move, the monsters move, too. This is one of those puzzle games that will send you running to the local forums in terror because the puzzles are so ingeniously hard. I am not kidding. There are also retail versions of this game and several sequels, but this is an excellent starting point to this series. Did I mention it's crazy hard?
Bricks and Bricks Jr.- Speaking of super-hard, here's another series I recall. Bricks is basically like those sliding tile puzzles, but they add stuff like holes, switches, magnetic blocks and other gimmicks to rack your brain and drive you nuts. Unlike DRoD, though, the forum forbids posting solutions, so you'll have to do this on your own. Bricks Jr. is an easier version of the game, but can still be pretty tricky.
Hydorah- A Gradius-styled shmup, and just as hard. Have fun trying to beat it! ;p
Battle for Wesnoth- A hex-grid strategy game, kind of like Fire Emblem meets Warcraft. Units level up as you fight, and in addition to the various campaigns, there's an online mode as well, and some user-made content as well.
I also suggest checking out Bytejacker's site, they cover indie and downloadable games like this, both free, flash-based and downloadable.
