Adding to MMario's listing:
Illinois - Illini (a prominent tribal group when the Europeans            arrived)

Florida - Floridian, Seminole, Gator or Hurricane

Wisconsin - badgers

Iowa - Iowan (a prominent tribal group at the time the Europeans             arrived), or Hawkeye

Taxas - some folks there prefer "Texican" or "Tejano" (tay-han-o)