Darn, Chris, you beat me to An Untitled Story.
Definitely worth playing through; I hope everyone here gives it a try.
I've not played this one yet, but
Within a Deep Forest looks like a pretty neat game. I've heard good things about it and intend to play through it sometime soon.
While I suspect it is probably not the cup of tea of most people in general, I'm a huge fan of
I Wanna Be The Guy, a brutal freeware game where nearly everything can kill you. It features a lot of NES game settings, which is pretty neat, and it has a pretty decent number of secrets to uncover.
Another neat freeware game is
Gravitron,
but I warn you that the file supposedly contains some form of adware, much to the confusion of the guy who wrote it. For those who care about that (hopefully everyone) but still want to give it a try, you could try running it inside of a sandbox. I recommend
sandboxie, a largely freeware app (has a 5 second nag after a month) for running potentially malicious software such as this, though it only works in XP. Ignoring any potential adware issues, Gravitron is a pretty fun game in the spirit of Gravitar, a fantastic Asteroids-with-gravity arcade game from the early 80's. Gravitron 2 looks absolutely phenomenal, but it's not free. Based on the trailers, though, it's probably one worth picking up, if this sort of game appeals to you.
Some others that come to mind that I've not put much time into, but really intend to get to soon, are
Battleships Forever,
Spelunky,
Eversion, and
Warning Forever.
That's it for now.