John Ford shot a lot of movies in Monument Valley (10 in all!), many with John Wayne. Stagecoach, The Searchers, Fort Apache, She Wore a Yellow Ribbon, My Darling Clementine, etc. Ford's films are so associated with this area, that the locals even named a spot after him (see pic above).
Of course, Ford isn't the only filmmaker to use Monument Valley as a backdrop in his films. Other films to feature scenes shot on location there include: 2001: A Space Odyssey, Once Upon a Time in the West, Forrest Gump, Back to the Future III, Thelma & Louise, National Lampoon's Vacation and The Eiger Sanction, plus many more.
Of course, as great as this place looks on film, it's 10 times more impressive when you're actually there.