[PROTOTYPE] is sort of like that. You start the game with a bunch of powers you don't know how to use properly, then you start a few weeks in the past with few powers and slowly work your way up to the super-powerful person you saw you could be in the beginning. It's not the most exciting game in the world, in fact it's pretty repetitive and has little replay value, but it's pretty much exactly what you're looking for and should last you a solid week or so.
Yea, prototype-like gameplay was pretty much what I was getting at. Excellently done. The first thing you learn to do is running up walls. Then you go on to flying. And by the end, you're just this big killing machine. Shame it didn't last longer. And the big muties were a pain in the ass.
Maybe I'll check out InFamous. Hear that's kind of similar.