Stagecoach
Red River
Winchester 73
Shanandoah
The Three Godfathers
Butch Cassidy and the Sundance Kid
The Treasure of the Sierra Madre
Magnificent Seven with Steve McQueen
The Searchers
The Wild Bunch
The Ox-Bow Incident
Cheyenne Autumn
THe Man Who Shot Liberty Valence
Hondo
Rio Bravo
The Cowboys
These are all classics. The more action oriented will be the Wild Bunch, Butch Cassidy, Cowboys, and the Searchers.
Try Two Rode Together, Duel at Diablo, and the Comancheros. These weren't on the list but great movies. Any on the list that have John Wayne are great westerns, but the best ones with John Wayne are The Searchers, Red River, and Rio Bravo.
Note: Treasuer of the Sierra Madre really isnt a western. Sorry to get technical, but just wanted to point that out.