Any one of Kurosawa's more famous samurai movies could be recommended, but Yojimbo is probably the best one to watch, if you haven't seen other Kurosawa flicks. Mifune's character not only influenced the Man With No Name, Sergio Leone's Fistful of Dollars is actually a remake of this film. So if you liked Fistful, watch it. If you haven't seen Fistful, watch it, then watch this. Both films are great.
After Yojimbo, I'd heartily recommend another Kurosawa classic, Rashomon [http://www.imdb.com/title/tt0042876/]. It really is the kind of movie you won't see in today's Hollywood. It's ten years older than Yojimbo, which shows in it being less influenced by western cinema, when compared to Yojimbo.
The plot is quite simple. A bandit kills a samurai in order to get down with the samurai's wife. This crime is then told through the eyes of the bandit, the woman, and other people, each telling the same story, but they never quite add up, as people tend to saturate their stories, intentionally or not.
It features some Japan weirdness, especially at the end, but it's a great movie, and stands out for being different, yet not pretentious, nor intentionally weird.