Democracy would collapse as any sort of meaningful political ideal.
When certain individuals are clearly superior(with both the brainpower and strength to back it up) why would they want to obey the powerless masses? Even if the Prof. X's of the world would submit to it, the Magneto's wouldn't.
I think a sort of neo-feudalism would tend to emerge, as nations collapse, and populations fall in under one super-powered being or another.
There would also be a huge surge and revitalization of the eugenics movement(if superpowers can breed true) creating a new institutionalized racism worldwide, as everyone tries to breed better, more powerful individuals.