The Gunfighter, with Gregory Peck as an aging fastest gun drained by the constant challenges to the title.
There ought to be at least two other sub-genres to consider, over and above the comedies:
Sci-Fi/Twilight Zone/Fantasy Westerns: Westworld as an example
Westerns to avoid: Missouri Breaks as an example
The Ox-Bow Incident goes somewhere like that.
The Tin Star is also a candidate.
I’m wondering why Dances With Wolves hasn’t been touted. (I’m not touting it, just asking.)
My all time favorite, among the many great ones previously mentioned:
Aaaack! Completely forgot about the most recent Western I saw - Dead Man. What do you call post-post-modern? I cannot think of a single bad performance in the entire film. Definitely one of my new favorites.
No worries. That film can never be recommended enough. Great minds think alike and all that…
American Westerns:
Butch Cassidy and the Sundance Kid (1969)
Cattle Queen of Montana (1955)
Clash of the Wolves (1925)
The Great Train Robbery (1903)
Heaven’s Gate (1980)
Hell’s Hinges (1916)
High Noon (1952)
How the West Was Won (1962)
Johnny Guitar (1954)
The Living Desert (1953) documentary
The Magnificent Seven (1960)
Man of the West (1958)
The Man Who Shot Liberty Valance (1962)
Melody Ranch (1940)
My Darling Clementine (1946)
The Naked Spur (1953)
The Outlaw Josey Wales (1976)
The Ox-Bow Incident (1943)
Red River (1948)
Ride the High Country (1962)
Rio Bravo (1959)
Rio Grande (1950)
The Searchers (1956)
Shane (1953)
She Wore a Yellow Ribbon (1948)
Stagecoach (1939)
3:10 to Yuma (1957)
The Treasure of the Sierra Madre (1948)
Unforgiven (1992)
Wagon Master (1950)
The Wild Bunch (1969)
American Northwesterns:
The Gold Rush (1925)
The Chechahcos (1924)
In the Land of the Head Hunters (1914)
McCabe & Mrs. Miller (1971)
American Northeasterns:
The Last of the Mohicans (1920)
In spite of the OP asking for good Westerns, now that Walloon has opened the flood gates, I feel compelled to list some of the B Western stars whose movies spanned the decades of the 30’s through 50’s with some trickle-over into the 60’s and certainly into the TV western series that basically rendered them obsolete. As a youngster I saw these guys on the big screen. The generations after mine saw them on TV in the afternoons, and can still see them on specialty channels even today.
Just some of the greats:
Allan “Rocky” Lane
Bob Steele
Tim Holt
“Wild” Bill Elliott
Sunset Carson
Jimmy Wakely
Hopalong Cassidy (aka William Boyd)
Roy Rogers
Gene Autry
Lash LaRue
Whip Wilson
Charles Starrett
Larry “Buster” Crabbe
Duncan Reynaldo (The Cisco Kid)
Rex Allen
Randolph Scott
Joel McCrae
There must be dozens more, but these are just “from the hip” shots.
The First Travelling Saleslady–the only time you’ll see Carol Channing running off with Clint Eastwood!
Caveat: a really horrible movie.
High Plains Drifter gets my vote for the most surreal, and good) Western ever.
“Horrible” is subjective. I figure Bosda could judge that 5.4 for himself.
Although it’s rather dated, being among those sprawling epics like Giant (which is one of the “modern Westerns” in location only), one I can recommend is The Big Country which has some big names and a big story. Charlton Heston, Gregory Peck, Jean Simmons, Carroll Baker, Charles Bickford, Burl Ives and some others who were regulars in the genre. Big in scope.
Fonda looked like he loved every minute of that movie. It couldn’t have been easy, turning the twinkle in his eye to an evil gleam.
Same with Gregory Peck doing Duel in the Sun, famously aka Lust in the Dust. Way out of character. Joyously evil. 
I was going to recommend some Randolph Scott titles, but it always takes half the movie before I stop thinking that a guy who looks like him has to be a bank president, and he wandered onto the wrong location.
The Shootist.
Of course it’s subjective. But it seems to me that the most helpful, to Bosda, would be suggest “essential” titles, assuming he can work his way out from there. Do you, honestly, subjectively, consider The First Travelling Saleslady to be an “essential” Western? A starting point? I understand that some people will like it more than I do, but it would honestly surprise me if there were a lot of people who considered it, in the history of Westerns, to be one of the essentials.
Just sayin, talkin bout the signal-to-noise ratio of this thread, an’ all.
Only for the novelty factor that I mentioned earlier.
She Wore a Yellow Ribbon is vastly underrated, and one of John Wayne’s best roles. He was pissed he didn’t get an Oscar nomination for it, and he was right.
Not mentioned in another Wayne/John Ford film: Fort Apache. Different in that the cavalry commander (Henry Fonda) is a jerk, and that the Indians aren’t the bad guys. It also shows what Ford had to say in Liberty Valance, that when the legend becomes the truth, print the legend. Wayne has to come to that decision, making a great film.
The Angel and the Badman is another good Wayne film, especially when he is forced to become a pacifist.
I’m surprised True Grit hasn’t been mentioned.
Finally, there’s Yojimbo. Sure, it’s not technically a western (it takes place in Japan), but it plays like one. A Fistful of Dollars is one of several remakes (Bad Day at Black Rock is similar, and Last Man Standing is a remake), but you should see the original (which, in turn, is based on Dashiel Hammett’s book, Red Harvest.
Destry Rides Again (the original and remake are great)
Winchester '76
Bend in the River
The Man From Laramie…as you can tell I think any western with james Stewart is a classic.
Also,the Wild Bunch,Tombstone and…Zorro,the Gay Blade!
I’d consider any John Ford Western essential I love **Cheyenne Autumn ** the most. It always makes me giggle to know that the Cheyenne in the movie are speaking Navajo and not Cheyenne.
How about the Lonesome Dove miniseries and its sequels?