I've recently run across a platformer called Eversion. At first glance, it looks like a kid's game, but deceptively so.
Its cutesy appearance hides genuinely difficult jumps, puzzles and cleverly-placed hazards.
The main idea behind it is "eversion", where certain points in the level allow you to "evert" to another plane of reality where the physics change. Clouds become solid, you can pass through trees, etc.
The story is a basic "Collect all the gems and save the Princess". You have to collect all 240 gems before you can save the princess at the end. There are two endings on the free version, and a secret ending if you spring for the HD version.
The controls are very simple. Press Z or up to jump and X or space to evert. You can change them if you want. Eversion points are easy to spot. When you pass by them, the music and palette will change subtly.
Here's a couple of screenshots:
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The HD version, available on Steam for $5:
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You can download the game here.
The eversion mechanic reminds me of Mighty Switch Force (which has a similar mechanic, but some other elements as well, such as a weapon and puzzles). I'll probably try the free version, but the only incentives for upgrading to the one on Steam seem to be HD and an additional ending so unless its fantastic and worth it (though $5 is still cheap enough one could spring for it and wouldn't lose sleep over it) I might hold off on getting the HD version for a bit.
I forgot about this:
You can make your own levels, as big and convoluted as you want them to be. Or you can just download others' levels. There's a ton of them out there.
i can personally vouch for cave story, spleunky, nethack, barkley's as all great free ware games. La Mulana I actually didn't know was freeware until I actually bought it but it is a full graphical update and on steam. La Mulana if you want the hardest metroid vania experience ever then go for it but it is deep and I'm about a 1/4 of the through it at most. Tower of heaven also very good but I think it's just a flash game. I found Iji to be a bit of a letdown but I didn't get that far into it.