There are some good ones here that I would second - Dr Strangelove, Battle of Algiers, The Lives of Others.
My list is going to jump all over the place as I think of things.
If you don’t mind westerns - The Wild Bunch is one of my favorites. Gritty Sam Peckinpah movie starring William Holden and others. It’s about over the hill outlaws during the Mexican Revolution.
Once Upon a Time in the West is a fun spaghetti western. Henry Fonda plays an absolute bastard of a villain and Charles Bronson is also in it. Lots of close ups of eyes and harmonica music.
War movies? Gallipoli. Thirty something years after first seeing it, it still makes me cry. It’s the damn music score and the futility of it all - run faster, Mel Gibson! Stop the next attack in time! Another WWI movie is Paths of Glory. It’s early Stanley Kubrick.
Some Like it Hot with Tony Curtis, Jack Lemmon, and Marilyn Monroe.
Psycho, Rear Window, and North by Northwest - Hitchcock
I’ve been in a nostalgic mood for fantasy stuff from my early youth so I’m going to also say Dragonslayer. Special effects weren’t bad for 1981. It’s not as dungeons and dragonsy as more recent dragon movies.
Time Bandits. Weird Monty Pythonesque fantasy. David Warner has always played a great villain.
I don’t know how you feel about David Lynch. Blue Velvet has some great performances. Dennis Hopper is at his Dennis Hopperest. If you don’t mind surrealism I’d also throw in Eraserhead.
Tetsuo The Iron Man. It’s a Japanese film and it’s like Eraserhead filtered through cyberpunk sensibilities. Again, if you hate surrealism I’d stay away from it.
I like Kurosawa too. Rashomon, Throne of Blood, Ran, Seven Samurai, Yojimbo.
Dead Snow, because nazi zombie movies are fun. It also counts as a foreign film!