Rand had the insanity issue in Wheel of Time. He also suffered a wound that would never heal.
Jaime Lannister (I won't say more because people may be reading/watching the series)
Tyrion Lannister is a dwarf.
Brandon Stark is paralyzed from the waist down.
It's been done. Seems like George Martin seems to consider it a lot more than other authors, but its common enough.