IMDB, and he played John Wayne in every single one of those films. The man's acting range can be fairly compared to that of Michelangelo's David. And yet, here it is pitch perfect.
One of the reason for this is a pretty good script. While I won't say that the lines are razor sharp, they play to Wayne's strengths and are made more enjoyable by his bizarre drawl. Rooster Cogburn gets most of the good lines in the film, but the dramatic weight of the film is carried by Kim Darby (who later played John Cusack's mom in Better Off Dead). This shocked me the first time I watched this movie; who would have believed that a teenage girl in a John Wayne western would be anything but annoying? As a rule, westerns don't have much of a strong female presence; having Darby's character drive the plot shows how many opportunities westerns have missed. The other supporting characters don't get a whole lot to work with, in terms of script, but they rarely seem shallow, which probably has more to do with acting and directing than writing.
The film is about Mattie Ross (Darby) and her drive to bring her father's killer to justice. To accomplish this, she hires the meanest Marshall in the territory, Rooster Cogburn. That's pretty much it. Sure, country legend Glen Campbell (sporting the same haircut he has today) is a Texas Ranger that helps them on their mission, but it's a pretty bare bones plot. Cogburn is mean and drunk, while Ross is strong-willed and obstinate; the movie is about how their personalities clash and gel.
While the script is good and the plot is fairly plain, the acting and directing stand out. Of course, Wayne plays himself, albeit an older, crotchety version of his classic tough guy. But Darby does a good job as the obstinate young woman and her acting makes the growing connection between her and Wayne's character believable. They didn't do it all alone, though. Glen Campbell is okay, I guess. Initially, I thought he didn't do much in the movie, but his performance does help explain how Cogburn and Mattie Ross can get along, adding an everyman presence to a movie where the two main characters stray far from the norm. Dennis Hopper manages to not seriously overact in a small role. Robert Duvall (who apparently never had a full head of hair) does a predictably good job as a villain who just seems desperate, not evil. Villains in the 1960s are often over-the-top, mwa-ha-ha, twirling-their-mustache evil, especially in westerns. Here, Duvall turns in an understated but believable performance, as he has done so many times since. I credit most of these performances to director Henry Hathaway. If you have seen any of John Wayne's less famous movies, you know how terrible the supporting cast can be, even with a decent script. Being able to push Darby and Campbell to where their characters needed to be made this movie what it is.
This isn't a flawless movie, of course. A lot of it has aged poorly as the popularity of westerns has declined over the past few decades. John Wayne at his best still has the tendencies of John Wayne at his worst; I've seen toddlers that can play a more convincing drunk than him. The viewer is forced to invest a lot of their interest in Darby early on, and it takes a while to believe that it's going to be worth it, because she is pretty annoying without Wayne to counterbalance her. Still, this is an all-ages western that manages to be endearing, funny, and touching, even to those that are normally bored stupid watching westerns.