Salt of the Earth

The movie itself was blacklisted during the Red Scare. Which is reason enough but it really holds up and the politics are (unfortunately) still very relevant today.

#1 has to be Z (1969) by Costa-Gavras, about the fascist coup in Greece in the 60s. Comrade made, you can just feel the anger of all the people involved. People talk about old movies feeling slow, this movie fucking pops. You can watch the whole thing for free in good quality here, honestly if you're not all in after the first 5 minutes, or really after the title card that says "any similarity to real person or events is not coincidental; it is intentional" followed by the speech at the fash gathering in a smoke filled room, then you won't like it.

If you like that, his State of Siege (1972) is also a classic, about when the Tupamaro urban guerrillas in Uruguay abducted US torture specialist Dan Mitrione. Just total :based-department: stuff. Filmed in Allende's Chile.

I'll second the people who mentioned Casablanca and The Bicycle Thief.

Bridge Over the River Kwai (1957) and Wages of Fear (1953) are also cool.

A lot of older Hollywood movies are really good. Casablanca is a banger. Most of Hitchcock's movies are really good. The first horror film in a given genre is usually worth watching if you're a horror fan. Halloween for instance seems a little trite now because it's the OG movie everyone else was copying.

Kubrick's movies are generally really good. Dr. Strangelove is a classic about American insanity. 2001 is just beautiful.

Godfather is genuinely really good.

A lot of the old Errol Flynn adventure movies were a lot of fun. Errol was a great athlete and a lot of his stunts still look impressive today. If he'd been making movies in the '10s he would have been doing his own parkour.

The old Spartacus movie is a classic.

Citizen Kane is definitely worth seeing if you're more than casually interested in film.

One Flew Over the Cukoo's Nest. I'm not sure how it reads now but my understanding is that at the time it did a lot to bring the plight of people confined to asylums to public attention.

Bullit has hands down one of the best car chases in cinema. It was the first and few have matched it.

The Treasure of the Sierra Madre is a classic. Probably some cringe racism but you're going to get a lot of that in older movies.

Fantasia is just gorgeous. Pure visual porn.

Charlie Chaplin has a lot of great movies that are worth watching. Same with the Marx brothers. Chaplin's The Great Dictator has an interesting history. From what I remember he made it more or less on his own to try to convince American's that there was a moral duty to intervene in WWII to stop Hitler.

Tombstone is worth it just for Val Kilmer's performance as Doc Holiday.

The 1954 Godzilla is a masterpiece, both as the first Kaiju movie, and as a cautionary tale about the horrors of nuclear war.

The Battle of Algiers is a semi-documentary about the Algerian's final battle to through the French out of Algieria and re-take their country.

Nosferatu is a classic horror movie that really helped shape the genre.

The Seventh Seal is a gorgeous, challenging meditation on the inevitability of death.

Metropolis is one of the first and most influential science fiction movies to really go hard on grand visuals and design.

A Fistful of Dollars is arguably one of the best westerns.

The Day the Earth Stood Still is another classic cautionary tale about xenophobia and nuclear war.

Forbidden Planet is a gorgeous, thoughtful retelling of The Tempest as a science fiction tale. It's also the origina of the saucer shaped UFO myth.

Freaks is in a very strange place. It's a movie from 1932 that focuses on the performers in a circus freak show. It's a horror movie, and certainly exploits then popular disgust for disabled people, but it also manages to be sympathetic and humanistic towards the freak show performers. When it was re-discovered and re-evaluated in the latter half of the 20th century it was judged to be important both as a piece of film history and an example of the humanization of marginalize people in a time where they were openly despised.

The original Invasion of the Body Snatchers is a great look in to early cold war US paranoia about communist infiltration.

The FBI investigated and nearly shut down It's A Wonderful Life, which should speak in it's favor

Battleship Potemkin is regarded as Eisenstein's masterpiece.

The Good, The Bad, and The Ugly is another western classic.

The Terminator, Terminator 2, Alien, Aliens, Close Encounters of the Third Kind, ET, all classics of science fiction.

The Lord of the Rings trilogy is brilliant cinema.

The Matrix is a classic of cyberpunk.

Akira is a masterpiece that everyone should see.

Ghost in the Shell is another classic piece of science fiction.

Jurassic Park was a major innovator in the use of CGI graphics and is fun to this day.

Princess Mononoke, along with most Studio Ghibli movies

The Shaw Brother's Hong Kong Martial Arts movies have had a huge impact on action movies.

The Raid is popularly regarded as having some of the best fight scenes in martial art movie history and invented the "hallway fight".

Amelie is an extremely charming comedy

Heat is a heist movie with some great acting and amazing gunfights

Snatch is a classic British crime movie

Pan's Labyrinth is a beautiful movie by Guillermo del Toro that blends fantasy and horror

The Thing is a tight sci-fi horror thriller with excellent VFX

Trainspotting is a classic movie about the ravages of heroin set in Scotland.

Fargo is an iconic comedy.

The Mad Max series is well worth watching. The first one is a crime exploitation movie, but the second too are really about mutual aid and finding human connections in a hard world. It's a very different kind of post-apocalypse movie than hyper-indvidualistic power fantasies.

Pirates of the Carribean is notable for being a lot of fun, and for being one of the first successful pirate movies since the black and white era

The Iron Giant is a classic animated film about cold war paranoia and friendship

Stalker and Solaris are two of Tarkovsky's best

Reservoir Dogs and Pulp Fiction are two Tarantino movies that had a huge impact on the culture of the 90s

You might check out the original Shaft. It's a classic of the Blaxploitation genre and had a powerful effect on the culture

Rocky Horror Picture Show... Has a unique place in history. For a long time it was one of the very few portrayals of queer characters that wasn't overtly negative. That was very powerful at a time when the culture was incredibly, unrelentingly hostile. Also has great songs and is just genuinely goofy fun.

I'm going to put in a good word for Dead Land. It's a movie from Aoteroa set before the arrival of Europeans. It follows a young Maori boy who sets out on a grim quest for revenge with the aid of a mythical, cursed warrior. I'd classify it as a Maori martial arts revenge movie, and I don't think there's really anything else like it. One of the best martial arts films I've ever seen.

Crouching Tiger Hidden Dragon is one of the finest Wuxia movies of all time and brought the Genre to western attention.

Y tu mama Tambien is a powerful coming of age movie with some queer themes that was very well regarded

The original Italian Job is a classic