I'm interested. Have an idea for a power based around 'stubbornness'. Stubbornness writ large. Someone so bullheaded that such things as being shot or crushed or stabbed or being set on fire is met only with "For me, it is not so". Or a much more confrontational "And WHAT!?!?!" depending on the circumstances. Depending on how broad these powers are supposed to be, you could also flirt with ideas of Solipsism, where my refusal to accept and acknowledge that that thing just happened means that it... didn't.

Picture an amnion of fizzing, electric energy surrounding a person that ley energy just boils off when it hits. Solid objects fraying and dissolving upon contact. Someone flinging a car and the car just stopping and dropping like it hit a concrete wall. Once the user had gotten used to his powers, anyway. At first it would be more like punches stopping dead and being able to force a locked door to open by pushing hard enough.

If we're going for "game designy" type powers, some sort of mechanic where it is linked to how frustrated the user is right at the moment. The longer the battle goes on and the more the opponent continues to fight, the stronger the effect gets. You'd get a character who was weakest at the start of the fight. You'd have to be sure you could take him down with your opening attacks, because if you didn't he would only get stronger and harder to kill from then on. As a weakness, it might even be completely deactivated in a situation where the user was not being openly confronted by someone (eg: not combat)

Other, more esoteric applications, the kind that wouldn't occur to someone whose power is that they are so bullheaded reality warps to fit - the kind of application it would take roleplay to get, in other words - would be "counterspell" type effects, or the ability to neutralise or dispel long-lasting powers. More subtle and nuanced applications of the Almighty Getting My Own Way Field.

As a bonus, would probably be a good complement to the more controller-type powers other people seem to be interested in playing.