I was a Cinema Studies minor in college, so some of these films may definitely seem obscure or just really old. I tried to pick the ones that piqued my emotions in some way. Sorry if I post movies that have already been mentioned in this forum. I also wrote some notes at the end of each film in case GC has standards for the films they watch too.
Paths of Glory (Stanley Kubrick, 1957)
A war film with an interesting twist on the genre. Minimal blood, black and white film.
Sword of Doom (English Title) (Okamoto Kihachi, 1966)
Samurai film with a morally questionable main character. Bloody, black and white film.
The Great Dictator (Charlie Chaplin, 1940)
Charlie Chaplin film with sound. A comic take on a country resembling Nazi Germany. No blood, black and white film.
Ghost Dog, Way of the Samurai (Jim Jarmusch, 1999)
Film about a modern day assassin who follows the samurai code. Short and few action sequences, but a good film nonetheless. Bloody, has harsh language, color film.
These are just a couple off the top of my head. I'll post some more when I remember good ones.