I'm not as big a fan of the pure Western as some are, though I believe a lot of those elements exist in other genres, Sci-Fi and Fantasy to name a few. I guess the only reason I'm prefacing is because I don't feel like as much of an expert about this topic, so lucky this question asks for a 'favorite' list, not a comprehensive best of. That would be difficult because I don't particularly enjoy John Wayne, which if I understand correctly, means my penis-looking thing is actually a vagina.
(To be clear, here is a brief list of Westerns that I don't love: The Searchers, The Man Who Shot Liberty Valance, Rio Bravo, High Noon, Once Upon a Time in the West, The Shootist, the remake of 3:10 to Yuma, the original True Grit, Django Unchained, How The West Was Won, Silverado, Cat Ballou, The Gunfighter, Rio Grande, The Assassination of Jesse James by the Coward Robert Ford, Lone Star, Hondo...get the picture?)
My Favorite Westerns
20) Sukiyaki Western Django (2007) Takeshi Miike, creator of such turbulent awesomeness as Ichi the Killer, Gozu and Audition, brings his insanity to the classic warring, small town factions fable.
19) Maverick (1994) Before Mel Gibson was a crazy person, he was an actor. A good one. This Western is fun as balls, handled by Richard Donner. The movie, not the balls.
18) The Proposition (2005) Australia had a turn-of-the-century as well, apparently. This movie's got Guy Pearce, Danny Huston and Ray Winstone. It's a dirty one.
17) Quigley Down Under (1990) I've professed my admiration for Tom Selleck's work in this movie - and Mr. Baseball - numerous times on blog.
16) Dead Man (1995) Before Johnny Depp was a home wrecker, he was an actor. This is Jim Jarmusch being his Jarmuschiest in black and white.
15) Blazing Saddles (1974) You really going to argue with this being on here? You're disrespecting Gene Wilder!
14) The Quick and the Dead (1995) Sam Raimi's ridiculous romp into the tropes of gun fighting. Equal parts dumb and silly and great. The cast really makes this one, with Leo and Russell Crowe and a dastardly Gene Hackman (and a less dastardly Lance Henricksen).
13) The Last of the Mohicans (1992) Only reason this isn't higher is because technically it's not a Western like the others, taking place in an earlier time period. For those who wouldn't have cared, pretend it's higher. I don't own you.
12) Dances With Wolves (1990) Epic Kevin Costner movies have gone the way of scalping. This one's the best of the bunch. Compared to Waterworld and the Postman you ask?
11) Slow West (2015) The most recent movie on my list, this is Michael Fassbender and Ben Mendelssohn doing western things in a totally non-modern way. I think I'd buy Fassbender as just about anything.
10) Young Guns (1998) Fuck you. This movie is actually good. And everyone from your eighties' masturbatory fantasies is present.
9) Butch Cassidy and the Sundance Kid (1969) People love these two fuckers, and the only reason this movie isn't a tad higher is because I have a particular problem with it. I think Newman is too good. So good I don't find the characters equal, and I don't buy into their camaraderie the way others do. Weird, huh?
8) The Good, the Bad, and the Ugly (1966) I'm not as big a Sergio Leone guy as most big time Western fans. This is the best one, right?
7) The Wild Bunch (1969) Peckinpah is another guy I don't love like the purists, but he gets it right in this one. Borgnine for the win.
6) True Grit (2010) Fuck yeah, the Cohen Brothers! This is my idea of a good time all around.
5) Appaloosa (2008) Ed Harris directs himself...need I say more?
4) Open Range (2003) Kevin Costner keeping it simple and straightforward, with Robert Duvall killing it every which way as per usual.
3) The Magnificent Seven (1960) These guys are pretty cool, though I still wish Yul Brynner had been playing his character from Westworld. That would've made this movie amazing.
2) Tombstone (1993) "I'm your huckleberry."
1) Unforgiven (1992) This is a fucking landslide victory. I think Unforgiven is one of the greatest movies ever made.
Short Answer: Good chance I missed a few. I always liked Hang 'em High, but I get all those Eastwood-starring Westerns mixed up, so I choose not to include any of the lesser ones. Plus, he could dominate the list, and that wouldn't be fun. Still, films like Josey Wales and Pale Rider deserve a shout out. And maybe, while I'm at it, an honorable mention to Shane. Shane! Don't go, Shane, you piece of shit! Fuckin' Shane!!!