There were so many movies and so many TV shows that it's really hard to pick one that standout above the others, even the shootouts. Still, there are memorable moments for a lot of them. Someone mentioned Glen Ford. There was some western he was in where the bad guy was trying to get his land or something. That plot accounted for half of all westerns anyway, I think. He had a faceoff with the bad guy and said something like, "you won't like the way I fight." He let the bad guy's gang burn down his ranch house, then ambushed them on their way back to town. But I don't remember the name of the movie, which I shall dutifully look up.
Again I don't remember the name of the movie but it's the one with John Wayne, Ricky Nelson, Walter Brennan and Dean Martin. There are a couple of good shootouts in that one. Maybe not very realistic but that's not what we're looking for in the movies. I get all the realism I can handle in my real life.
Shoot low, sheriff. They're riding Shetlands!
Underneath the starry flag, civilize 'em with a Krag,
and return us to our own beloved homes!
Buy War Bonds.