As a big cinema buff who has enjoyed a wide array of foreign, indie and cult films for a big part of my life, that's a tough one...in no particular order tho:
Jan Svankmajer's Alice, Little Otek, and Faust(Alice is a personal favorite tho)
Anything by David Lynch, especially Eraserhead, Blue Velvet, Twin Peaks & Lost Highway
Waking Life
The Fall
The Cell
True Stories
The Dark Backward
A Town Called Panic(french, stop motion)
Gummo
Julien Donkey Boy
Brazil(Anything Terry Gilliam really)
The Taste of Tea(GREAT Japanese family film)
Beetlejuice
The Reflecting Skin
The Brothers Quay: Streets of Crocodile
Paprika(Japan)
Funky Forest(Japan)
Symbol(Japan, 2009)
Holy Mountain
El Topo
Six String Samurai
Meet the Feebles
2001
One Hour Photo
Palindrones
Happiness
The Wizard Of Space And Time
Tokyo Fist
Begotten
The Secret Adventure of Tom Thumb
An anime called Paprika comes to mind. I haven't seen it since I was a senior in high school and I've only seen it once, but I just remember watching it with my good friend and saying to her "...What the frick are we even watching?" I love certain anime movies, but I just remember finding that one particularly weird.
And The Room is pretty weird. And awful.
Paprika was great, saw it in theaters. I lovvve mind bending stuff like that^^