I'm going to restrict this list to older movies and imports since there's already most of Hollywood's best listed by other people.

• Ran (1985): Japanese take on King Lear. Kurosawa.
• 12 Angry Men (1957): Fonda has doubts about the man charged. Sidney Lumet.
• Lawrence of Arabia (1962): Based on actual WWI British officer T.E. Lawrence, but more story than history. David Lean.
• One Flew Over the Cuckoo's Nest (1975): Jack Nicholson leads this Milos Forman movie about what it was like in mental hospitals (based on Ken Kesey's book of same name -- see also Keroac book On the Road for more of that generation).
• The Man Who Would Be King (1975) : Sean Connery and Michael Caine star in John Houston movie based on Ruyard Kipling story. There are more famous names to pack in there, but mostly the story is great (though told from a supremely Colonial POV).
• Grand Illusion (1937): French Jean Renoir film classic about WWI.
• Beauty and the Beast (1946): French Jean Cocteau masterpiece of the fairytalke before it got Disney-fied.
• The Tin Drum (1979): German Volker Schlöndorff film of Günter Grass story about a boy who won't grow up.
• Amarcord (1973): Italian Federico Fellini film about growing up. You could sub in Nights of Cabiria or Satyricon as a starter Fellini pic.
• Kes (1970): British Ken Loach film about a boy and a bird.
• Winter Light (1963): Swedish Ingmar Bergman about a priest struggling with faith. The 7th Seal probably a better place to ease in to Bergman, though.
• A Man for All Seasons (1966): British Fred Zinnemann telling of how Sir Thomas More was stuck between his Church and his King. For an alternate take on same chunk of history, see Wolf Hall.

There's so many more. Rosselini's Open City, Jodorosky's El Topo/Santa Sangre, Errol Morris documentaries (Fog of War, etc.), Les Blank docs (from music to Werner Herzog Eats His Shoe), oh! and Herzog flicks! I should stop.