Too many to choose from to pick just one, so I'll just list one from each decade knowing I won't win for ignoring the rules (btw: I just received the new McLintock in the mail today, so just responding to provide my favorite Wayne westerns).
"Stagecoach" for all its brilliance, with honorable mention going to "Winds of the Wasteland": Of all the earlier "B" westerns this one fits just right for me. The stagecoach race at the end is excellent to watch. Sure would like to see Olive (or somebody) release this one on blu-ray.
"Tall in the Saddle" has that feel/plot to me of the earlier "B" westerns with Gabby Hayes, but also has Ward Bond (a favorite) and a much higher production quality to it. Another I would like to see a blu-ray of.
"Rio Grande" is a great movie and I enjoy the connection between Wayne and Maureen O'Hara, Since i can't choose "Quiet Man" I will go with this one.
"El Dorado" just works better for me than "Rio Bravo", maybe it is just Mitchum and Caan vs. Martin and Nelson that swings the vote this way. Honorable mention to McLintock! (more Maureen O'Hara).
"Chisum" or "Rooster Cogburn", I can go either way at this point.