Phantom of the Paradise is unlike any film I have ever seen, it's kind of unique Nicholas Winding Refn's Valhalla Rising is also quite unique, the main character never says a word and a lot is left open to the viewer to interpret. Stalker of course (Tarkovsky) is another one where there is very little dialogue, hardly any exposition, and lots of long takes and it's up to the viewer again to interpret what is happening. Robert Eggers is probably the most unique film maker working now with things like The Witch and The Lighthouse.
Don`t know if it`s already been mentioned but `The Fall` has to be the most beautiful film ever made, pause any frame print it out and hang it on your wall.......
Love the book, loved the television series, love the movie: nice to see it get a mention here because it's generally regarded as a disappointing film. Great movie but I think inferior to (and very similar to) Kagemusha. Great movie but the hard boiled thriller is a genre and I'm not sure that it sticks out as exceptional. Get Carter would be my choice along those lines. There are a lot of great calls in this thread: yes, 2001; yes, Peter Greenaway; yes, David Lynch (although I don't rate him as highly as some in this thread). You can't copy Memento in any way without its being completely obvious, although you might say the same about Groundhog Day or several other high-concept movies. I think that there are a lot of great answers but I think I'll add my favourite film of all time: Being There.
Two that I have not been mentioned here so far: Ken Russel's The Devils (NSFW extended trailer linked here) https://youtu.be/HWGmXF5Dqpk Begotten
Begotten seems interesting. On one hand it's not unique, given that it looks like it was filmed 110 years ago, but on the other hand that's one of the things that makes it unique in 1989. I'm wondering if I should watch it. I'm not trying to be funny here; it looks like it should have a Norwegian Black Metal soundtrack.
The complete movie is on Youtube and not hard to find. I believe this movie has only ever been released on DVD and an original non-bootleg is pretty hard and expensive to find. It's deliberately shot in that grainy b/w hallucinatory style and really is a near-silent film with no dialog and little more than discreet ambient background noise (crickets chirping, running streams, squishy sounds, etc) and very occasional ambient music. The near silent soundtrack coupled with the vague imagery and abstract plot typically draws the viewer in and ultimately leads to a pretty disturbing viewing experience if you can make it through the whole film (most people I know who've seen it give up on it fairly quickly).
Last night I watched one of the strangest, craziest movies that I've ever seen, Lake Michigan Monster. It's as if you took a heathy dose of early Woody Allen, Monty Python, and Casper the friendly ghost's rude sister and made a movie. It's shot in B & W. It has periods of animation. It has a sea captain that is not a sea captain who's quite funny. He leads a team of four looking to kill the monster.
I've watched Upstream Color and it lost me - I need to take another crack at it. Another that deserves mention is Primer - it is probably the most realistic in the "time travel" genre if that makes any sense. You have to pay attention but one you grasp the concept a little light bulb will go off in your head. Another brilliant film that requires you to think.
I will add some more unique movies to the list: Haiku Tunnel Time (a movie from South Korea) 9 Anormalisa Hero Jack And The Cookoo Clock Heart Hidden Heroes
I was going to mention Stalker and Valhalla rising. Both are favorites and unique. The Return (2003), a Russian film directed by Andre Zvyagintsev. It's a tale of two fatherless boys suddenly confronted with a Father, gone 12 years. Is mysterious as it unfolds and seems to be leading somewhere dramatic...and is unique in that you are given no answers or even given the questions.