Any list without The Magnificent Seven is incomplete.
Unforgiven is so good the Japanese remade it as a samurai movie. True story.
Tombstone, and not only for Val Kilmer's epic performance. Although Dana Delaney's performance almost ruined it. Sam Elliot, though.
Hombre is very good, but not Top 10. All due respect to Elmore Leonard, who is a God. For a Leonard Western, I prefer Valdez is Coming
Rio Bravo. Wayne at his best.
The Coen Brothers' True Grit. (This, I will allow, is a subjective choice. At least one of the True Grit movies should be on any list)
Outlaw Josey Wales, Winchester '73, GB&U, Butch Cassidy & SDK ("Who are those guys?"), The Man Who Shot Liberty Valance, The Wild Bunch.
I won't discount Red River, The Searchers, or Stagecoach, but my two (three including the original True Grit) favorite John Wayne movies are listed above.
I also won't argue with My Darling Clementine.
Edit: Ah shit. Forgot The Assassination of Jesse James by the Coward Robert Ford. So excellent. Pitt and the lesser Affleck with career performances.