It's the one where he plays Marshal Duncan or something like that and he winds up being betrayed and apparently killed. He spends three movies hunting down the guys who did it, and part of the whole schtick is that he comes riding into town in a heat haze, and disappears the same way. He does various things like paint an entire town red (including the church, especially the church) in the last movie, and the final confrontation makes it kind of clear he's not normal with people basically getting whipped to death off camera (like they did to him) and thrown through doors in record time to the point where it shouldn't have been possible. They wind up asking who he was but at the end he goes past his old grave and makes it sort of clear that he's the guy whose buried there.
The point was that it was supposed to be subtle up until the end, and it's a big topic of debate as to whether he actually survived his presumed murder, or was a ghost, but I believe it was stated several times by the director and Clint Eastwood that the character was basically a ghost. I believe it was also referenced as one of the big inspirations for "The Crow", both the stand alone comics, and some of the scenes in how the first (and by far the best) movie played out.
The point though is that unlike "The Crow" it can be argued either way, as he did some very human things, but at the same time it was also why he was able to do the crazy tough guy stuff, which while stereotypical for cowboy movies, was happening in a more gritty environment where others seemed to be playing by a different set of rules. Basically nobody could outdraw the guy not because they were going for pure cheese but because the guy was literally not human.
I could be wrong by I believe one of the old version of "Boot Hill" (that might be the right western RPG) statted out famous movie gunfighters for comparative purposes, and "The Man With No Name" has a 99 in speed and accuracy or something like that, which is basically impossible to roll or obtain, because he's not mortal. Basically if he draws on you your dead...