During the climactic Indian attack, the Ringo Kid climbs on top of the stagecoach, then makes his way to the lead horse of the team pulling it. Made doubly awesome since there's no special effects to it: that's really stuntman Yakima Canutt leaping from horse to horse at very high speed.
Canutt deserves more general mention; not only was he a real-life Bad Ass, he helped pioneer numerous movie-stunt techniques still used today.
The scene introducing us to The Ringo Kid. That's how most of the world got to meet John Wayne, and it's one HELL of an introduction.
Insufferable and corrupt banker Gatewood being arrested when the stagecoach arrives in Lordsburg.