For SF, I recommend Primer. Its definitely a challenging movie as there's no clear exposition, but I found myself wanting to watch it several times to piece it altogether.
Coherence dinner party among friends gets stuck between alternate realities. One of those really good scripts that was shot on a microbudget. Weird movie, lots of fun to think about
Prospect a western film about a prospector going after a big score which also happens to be a sci fi movie set on an alien planet. Great film, very cool style and very underrated.
Wings of Honneamise is an anime from the 80s that I rarely see mentioned that has a special place in my heart. It's about the first space program in some foreign world, with conflict and war that captures the frontier spirit.
Black Rain, directed by Ridley Scott and starring Michael Douglas and Andy Garcia, is not exactly some small indie movie but I never see it mentioned anywhere. I would describe it as a fish out of water story with two American cops going to Osaka. I love the movie and the soundtrack.
Colossus: The Forbin Project from 1970 is a sci-fi classic that I think really holds up.
A Taxing Woman from 1987, co-incidentally the same year as Wings of Honneamise, is a Japanese movie about a tax collector going after a criminal who is hiding his income really well. I caught this late at night on TV 30 years or so ago and just enjoyed it a lot.
The Extraordinary Adventures of Adèle Blanc-Sec is a French movie, bringing a comic of the same name to the screen. I really liked the comics already and the movie was fun as well. Early 20th century Paris, some fantasy elements.
Forbidden Planet, 1956, is also a sci-fi classic, starring a young Leslie Nielsen in a serious role.
The 1978 version of Invasion of the Body Snatchers is my favorite version of the story. It stars Donald Sutherland, Leonard Nimoy and Jeff Goldblum. You might have seen Sutherland from this movie as a meme.
La Haine is another French movie, starring Vincent Cassel, Very intense, very good.
Ladyhawke is a fantasy movie starring Rutger Hauer, Michelle Pfeiffer and Matthew Broderick. I wish there were more movies like this. Just telling a nice story. A cursed couple, a thief and a lot of adventure.
The Name of the Rose, with Sean Connery, Christian Slater and Ron Perlman, is a lovely version of Umberto Eco's book of the same name, that tells the story in an actually entertaining way.
The Ninth Gate with Johnny Depp is another book adaptation that I think is better than the book. Fantasy and mystery and suspense.
Oxygen is a French sci-fi movie with a really minimalistic set and cast that I was pleasantly surprised by.
The Patlabor movies are among my favorite anime movies. Mostly calm and mature characters and nice stories.
The Prophecy with Christopher Walken and Elias Koteas was an indie success in the 90s. Angels, the Devil and mortals caught in between.
Shin Godzilla (2016) is my favorite Godzilla movie of all time. I can see why people might not like it, but it just tickled me in all the right places.
Strange Days is one of the best cyberpunk movies out there.
Top Secret! is brought to you by Zucker, Abrahams, Zucker, who brought us, amongst other movies, The Naked Gun trilogy and Hot Shots. It's equally silly and funny.
Enter the Void is the most breathless barrage on the senses I have ever wittnessed. The intro could give you epilepsy. The whole film is shot from the ego perspective of the protagonist that gets shot dead 15 minutes into the film. I have never seen anything remotely similar.
Weird 70s animated sci fi: Fantastic Planet. The original is in French (which I prefer) but it also has an English dub. It's French sci fi from the 70s so this probably goes without saying, but in case anyone was considering a first watch with their parents or small children: there's a fair amount of nudity and sex.
If you haven't seen Wolfwalkers it's also worth a watch. It's by the same studio that made Secret of Kells, and takes place during the Tudor conquest of Ireland. This one is kid friendly, but I've watched it with a group of adults and we all enjoyed it.
For sci fi, Run Lola Run is a fun 90s era take on how small changes in starting conditions results in big changes for different timelines.
For comedy, I'll always recommend Grandma's Boy. It's a stoner comedy that focuses on a game developer and has a strong cast. It's from Adam Sandler's studio so you'll see a lot of familiar faces, but not Sandler.
For animated, try The Fantastic Mr. Fox. Great cast, Wes Anderson asthetic without being too twee, and a great script.
Tampopo - it's not really a comedy but has comedic elements. It's a overview of Japanese food and food culture and is one of the most beautiful movies I've ever seen.
Huge in China but not much in “the west”: Wandering Earth big budget, wild plot. A bit ridiculous but in an Armageddon or Pacific Rim kind of way. Good popcorn/summer movie.
Swiss Army Man (idk Daniel Radcliff is a farting, talking corpse. Movie about self acceptance? An elderly couple walked out of the theater after the opening credits when i saw it lol)
Kiss Kiss Bang Bang (Robert Downy Jr & Val Kilmer detective/noire)
The Naked Gun Trilogy (Leslie Nielson as a cop, idk how old you are but maybe you haven't heard of these)
Sci-Fi
Upgrade (quadriplegic man puts AI in his head)
Turbo Kid (Mad Max type dystopian future, one of my favorite movies ever but I've only been able to find it on YouTube or "free streaming". It's Canadian and their blu-rays don't work in the U.S.)
I feel weird recommending this movie because I fully acknowledge it's not exactly good, but...
The Man Who Knew Too Little (1997)
This has long been one of my all time favorite comedies. I've seen it probably a half dozen times, and it still makes me laugh out loud. Bill Murray is brilliant and Alfred Molina is clearly having the time of his life. I absolutely love it.
Best Polish SF movie is a comedy from the 80s abut two guys who are hibernated and wake up in a world without men. It was filmed during communism and it's full of hidden jabs at the system. It's actually a good SF movie.
For animated sci-fi, I'd go with A Scanner Darkly. It is about a future LA deep in a drug war that uses rotoscoping to lean into the feeling that not everything is right.
Deathgasm. It's about a bunch of metalheads that find some sort of old hymn. When played, it summons hoards of demons/zombies. So then they start fucking up the zombies. I vaguely remember one of them being impaled with a dildo? Either way, it was an entertaining "turning your brain off" watch that's pretty unknown afaik.
Iron Sky from 2012. It doesn’t have good ratings but the first time I watched it with my father, it was hilarious. Granted, the humour is quite dark but the cultural differences that you will come to see are so funny. I liked it, personally, but of course it’s not for everyone.
Creep (2014) and it’s sequel are some of the best horror movies I’ve seen from the last decade (not saying much, considering the genre is filled with stinkers, but still). They’re both presented as documentaries, and the characters are a little more believable than your average horror character.
I actually prefer Creep 2 over the first one. The protagonist in the first movie is compassionate to a fault and he makes some really dumb decisions. The protagonist in the second movie doesn’t take the threat seriously at the start, but once she realizes the danger she actually gets her shit together
The antagonist in both movies is a brilliant character, and you see some great acting on his part. The guy is an absolute mental case but endearing at the same time. His behavior is both deeply disturbing and hilarious
Blackbeard's Ghost. Watchable on Disney+ right now. Family friendly, great performances and some epic physical comedy from Peter Ustinov (voice of Prince John in Disney's Robin Hood).