Crackdown

Loved this game. It was kind of just GTA but you had super powers. They gave you some loose-as-can-be story and then gave you super power and were like "go kill criminals, dude". Then they added this kind of EXP system similar to what Fable had where depending on what thing you did you got more EXP of that kind. Shooting dudes? You get Shoot EXP. Makes you a better shooter. Then your dude started to look different based on the levels. Again, like Fable.

The best part-- the best part-- though was that there was like Jump EXP. So you basically had to climb all the buildings. Including the insanely tall HQ which you could only get up to if you leveled up enough. And it took forever to get all the jumps. But man so funny the most fun part of the platforming.