That's a cool thread! What I like the most about media from around the world is how different they treat similar stories and themes, filtered through their unique culture and way of life. Nice stuff.
I'll start with what I feel is cheating a little, since Japanese media is arguably the most dominant after US one, but two movies I'm really fond of are:
Hausu (1977)
This is one of my favorite movies ever. It's just really hard to explain. It's a movie about a girl named Gorgeous and her friends trapped inside a haunted house. That's kind of the plot. That's not the movie, though. It's crazy, unique, fun as hell and absolutely unhinged cinema. Nothing quite like it.
Audition (1999)
I feel like this was pretty well known in the day. A movie about a middle-aged salaryman whose wife died years ago and now he wants to find a new partner. To avoid all the work, he and his friend organize an audition for a radio program that doubles as a way for the salaryman to find a girl he likes without having to do the trouble to get to know her. He meets Asami and they start a love story together... until things go horribly wrong. It's a misleading movie. It has the baggage of having a really emblematic climax, a whole reputation, but the movie is much more interesting than only its most famous scenes. Greeeat movie.
Suicide Club (2002)
54 teenage girls commit mass suicide by jumping in front of a train. From there, a weird mystery about a supposed Suicide Club, whose members (all teenagers) keep organizing and commiting acts of mass suicide start to unfold. It's weird. It's funny and dark. But mostly weird.
Three offbeat and weirdly touching movies to me.
In music, I really love this Brazilian band called Carne Doce. Their last album is pretty neat.
In comics, El Eternauta is a masterpiece.

Seriously, one of the greatest comics I've ever seen. It's Will Eisner levels of masterpiece.