You can’t go wrong with The Good, The Bad, and The Ugly, or The Judge Roy Bean. Young Guns and Unforgiven are my favorites from the more recent westerns produced. And of course, I can’t forget High Plains Drifter.
“the” Best Western? My vote is for The Searchers, but not because it’s a Western, but because it showcases our three main characteristics - “mean, stupid and crazy.”
I think the American West is too big a theme for any one movie to do it justice (my proof: any votes yet for “How the West was Won?”) So I give credit to John Ford for making one film per aspect: blind hatred addressed in “The Searchers,” the taming of the West, in part in the above-cited church-building sequence of “My Darling Cementine,” and more fully in “…Liberty Valance.” A germ of the injustice to the Indians was in “Searchers,” and given full voice in “Cheyenne Autumn.” He devoted “Sergeant Rutlege” to the Black experience (schmaltzy - yes, but that experience has yet to be given due credit on film, “Buck and the Preacher” included.)
Even the Mexicans, heros in no Western of the era, were given recogition in “She Wore a Yellow Ribbon,” in the scene where the American column encounters a three-man Mexican patrol, and afterwards the Americans remark upon the Mexicans’ bravery for doing with three men what the Ammericans require of two hundred.
(BTW - one reason Ford was able to put in such scenes was because he wasn’t locked into the current Ridley-Scottish dogma that everything on the screen must contribute to the immediate narative. The scene in “Celmentine” where Victor Mature is reciting Shakespeare along with the actor adds nothing to the plot but everything to character expositon. Dopers, all drama is either character expositon, or it is Rildey-Scottish special effects.)
Some of my favs, in no particular order…
Dances With Wolves
Unforgiven
Wyatt Earp
Outlaw Josey Wales
Maverick
The Shootist
Silverado
BC and SD Kid (Newman & Redford)
Two Mules For Sister Sara
Could go on and on…
Wow…so many great westerns here…
Big Jake
The Searchers
The War Wagon
The Shootist
The Cowboys - incredible score by John Williams
The Cheyenne Social Club
How The West Was Won
Cheyenne Autumn
Support Your Local Sheriff
Support Your Local Gunfighter
Maverick
High Noon
Bad Day at Black Rock
The Ox-bow Incident
Some more favorites:
http://www.filmsite.org/westernfilms.htm
http://www.filmsite.org/westernfilms2.htm
http://www.filmsite.org/westernfilms3.htm
Most of the good one have been named, so I’ll add my vote to:
The Magnificent Seven
The Long Riders
High Noon
I have to add
Jeremiah Johnson
and
The Three Amigos 'cause it cracks me up everytime I see it.
** Eagle’s Wing ** 1979, Martin Sheen, Sam Waterson, Harvey Keitel, Caroline Langrishe. Story of obsessive struggle between white man and indian to possess a magnificent stallion. Slow and beautiful.
And how come no-one has nominated Lust in the Dust yet?? 
Watched Silverado over the weekend. Verrrry disappointed. The acting was wretched and the direction second rate. And there was a ton of gratuitous shooting. Lastly, Kevin Costner was in it. Arrrrrggggggg!! Please, no more Kevin Costner!!!
Rustler’s Rhapsody
If you haven’t seen it… go get it, especially if you enjoyed the Trinity movies.
Tom Berenger…mmmmmmmmmmmmmmm.
One–ONE???–mention of The Wild Bunch? Possibly the GREATEST American movie OF ALL TIME?!?!? Sheesh!
The Outlaw Josey Wales was Eastwood’s best. The Oxbow Incident was brilliant, easily Harry Morgan’s best movie, and I’m including the Support Your Local… movies. And The Treasure of the Sierra Madre with a brilliant performance by everybody except, not unexpectedly, although it was his best work, Robert Blake. (How would you like to have peaked before you were ten?)