If you haven't seen it yet, watch The Man Who Shot Liberty Valance ASAP. It's a great movie, stars both John Wayne and James Stewart!
For a change of pace, check out Support Your Local Sheriff and Support Your Local Gunfighter.
McLintock! is great -- the movie features John Wayne and Maureen O'Hara.
Big Jake is a very interesting film. This is another of John Wayne's later movies, and takes place in 1909 so in someways it's like watching the twilight of the wild west.
A Big Hand For A Little Lady -- It's a great movie and well worth watching; Henry Fonda is the big star in the movie. Please avoid the wiki article (and other potential spoilers) if you intend to watch the movie.