In the vein of musicians, Oklahoma has a bunch of country musicians: Garth Brooks, Carrie Underwood, Blake Shelton, Reba McEntire, Toby Keith, and Vince Gill. Woody Guthrie was also from Oklahoma. In addition to the mentioned Flaming Lips, the Kings of Leon are from Oklahoma.
Will Rogers was from Oklahoma. Astronaut Shannon Lucid is also from Oklahoma.
On the entertainment front, Brad Pitt, Chuck Norris, Ron Howard, James Garner, Rue McClanahan, among others.
Sports wise: Mickey Mantle, Johnny Bench, Jim Thorpe, Bill Goldberg, Blake Griffin, among others.
Wilma Mankiller is pretty awesome.