Braid

 Braid is a platformer that plays with time.  You and some limited objects have an unlimited amount that you can go back in time.   So it's a matter of unravelling what the level offers you and traversing it in a Mario'ish way using this mechanic.

The point where I gave up on this was when it started getting to be about execution time.  You can speed up your reversal in order to be at a certain point where the scene caught up, and getting that precision correct can be a bit annoying.  

You are trying to collect puzzle pieces and assemble what you found like a jigsaw in some hub levels, but I never completed an image to see what it did...