I'd like to recommend "The White Chamber".
http://www.studiotrophis.com/site/projects/thewhitechamber
Gameplay-wise it's your standard issue 2D point'n'click adventure, old-school lucas arts style. Nothing new or innovative there...
BUT... the story is rather mysterious and outright psycho... combined with some creepy sound, this makes for a dense atmosphere you rarely get to experience in a game.
Another suggestion would be Ufo2000.
http://ufo2000.sourceforge.net/
This is largely a rip-off of X-Com: Ufo Defense that only features the squad-based battle part (missing the base-building, economic part) but introduces 1on1 multiplayer, and enhances the tactical abilities of the game, to make it better suited for multiplayer battles. The amount of different play strategies players did come up with is amazing.
It does have this special quality i do admire about chess: Everyone can play it a little different, and still be good at it, his own individual way. And sometimes, being unpredictable is worth a lot more than just knowing the "best" strategy.
I've played my share of indie-games and will continue to do so. And most of the real garage stuff just doesn't make you want play it for more than one day. Heck, i put away many of those games after less than an hour. Crappy gameplay, tons of bugs, "unfinishedness" and frustrating controls are quite common. But there are some gems out there, worth searching for. Games that make you realise how bland and dull those mass produced mainstream titles mostly are. "Shallow" is the perfect term i guess.
have fun
PS: It's a shame so many indie titles want to be just like their "role models" (08/15 AAA titles) soooooo much, they completely forget about beeing unique in any way...