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Binding of Isaac is pretty great. There's the initial sense of discovering everything for yourself, and you realize it gets more and more nuanced, and then once you have everything under your belt you realize it's a tight little dungeon crawler. Super Meat Boy's also a pretty good challenge-platformer. (Edmund McMillan's a pretty cool dude; he Skyped the AGDQ marathon and shot the bull about game design while they demolished his game in a few hours.)
These are some really common suggestions, but:
Jamestown's a good shooter with a pretty funny style behind it and some nice challenge levels.
http://www.finalformgames.com/jamestown/
The Stanley Parable has both a great sense of humor and a nice tongue-in-cheek look at video game story structure. Only takes an hour or two to complete, and I don't know anyone who didn't enjoy it in some regard.
http://www.moddb.com/mods/the-stanley-parable
Seriously, just go play it. Now.
Cave Story is a linear and (early on) a backtrack-heavy Metroidvania-styled platformer. That's about the worst I can say about it, considering just about everything else about it is great, from the pseudo-16-bit graphics and great music to the nicely floaty controls. Also free. (You don't need to get +.)
http://www.cavestory.org/
Iji's the same way, a linear platformer kinda like Cave Story. Less on the backtracking and more on the cool atmosphere. Lots of detail all over the place, and I think the only game I've liked the implementation of a "moral system."
http://www.remar.se/daniel/iji.php
VVVVVV's a really damn simple but well-executed platformer. Fuckin' amazing soundtrack, too.
http://thelettervsixtim.es/
Say what you want, but from a game standpoint alone, Braid's pretty good. Gets a bit stupid with some storytelling aspects, but the arguable metaphor for the story is done in a really cool way.
I haven't played it myself, but Sequence is an RPG rhythm game that I know a bunch of people loved.
http://store.steampowered.com/app/200910/
To the Moon's more visual novel than game in some ways, considering the good parts of it were from the story and not the interaction. Still pretty great.
http://freebirdgames.com/to_the_moon/
Yume Nikki's a very unnerving exploration game. I've lost more sleep over it than Amnesia, at least.
http://www.mediafire.com/?98jpx2dm3f2te0h
Eversion is a thing.
http://zarat.us/tra/offline-games/eversion.html
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