Here come a couple of 'em, all Japanese classics.
Rashomon (1950)
Great, great movie. So simple in its premise, yet very potent.
Yojimbo (1961) and Sanjuro (1962)
Yojimbo ispired A Fistful of Dollars (and the nameless main character) - they are almost the same, but different in that one is a samurai, the other from the Wild West. Loved both Yojimbo and Sanjuro, nice movies overall, the main character is great.
Ikiru (1952)
A man gets terminal cancer and we see what happens when he finds out up until his funeral. It gets better as it goes on, and the final act is just amazing.
The Hidden Fortress (1958)
Also very good. Bit more action than meaning but fun to watch.
...aaaaaaaand here comes the best of 'em!
Harakiri/Seppuku (1962)
Seriously one of the best movies I've ever seen. It's very simple in its premise and story, yet it hits on so many levels. Not a single move feels out of place, let alone a shot or a scene. And it just sucks you in, you just want to know what happens next, you get more and more invested. The scenography and camerawork are brilliant - also very simple, but for a B&W movie, amazing. Pretty universal as well. It's just a primer on how to make great movies and for me, one of the greats.