Some entries not on here:
Megaforce (Sort of the ultimate in 80’s sci-fi nonsense)
The Quiet Earth
Castaway on the Moon
Doomsday Book
Tetsuo the Iron Man
Being John Malkovich
No Such Thing
Burn After Reading
Tideland
Does it count, if it’s from one of the “Usual Suspects”?
i.e. A filmmaker well known for other “weird” movies?
Because that really pares my list down. Cohen Bros., Terry Gilliam, Spike Jonze, some Asian horror filmmakers…
Castaway on the Moon and The Quiet earth are awesome, not seen Megaforce but much respeck for Tetsuo. Don’t think I’ve ever managed to sit all the way through in one go.
Tideland makes me cry. 
Will be watching Doomsday Book and No Such Thing soon!
Ooh, The Quiet Earth!
I haven’t seen that in years!
(Wind hanging statement removed)
The reviews are almost more enjoyable than the film itself:
Tideland just creeped me the hell out. That’s what I remember most vividly about it.
Oh totes forgot about that film. That was a nice if a bit slow moving bit of oddness.
Megaforce I couldn’t get past the first 20 minutes the first time I saw it. It may be ‘better’ now that I can appreciate it for the awfulness.
And I just remembered
Uzumaki
Probably one of the most atmospherically creepy films I have seen. The manga is even more bizarre.
Few more off the top of my head:
Burt’s Buzz (Interesting for the stuff it shows you, but fails to acknowledge–it’s a Documentary, though!)
Henry Fool (Another Hal Hartley, all his films are “Weird”)
A Scanner Darkly (Philip K. Dick–of course it’s weird.)
Postal: The Movie (Great if you know the story behind the film)
Her
Welcome to Me
The Piano Teacher (Deviant, filthy, beautiful; French)
City of Lost Children
Into the Forbidden Zone
Blood Freak (Reefer Madness meets Giant Murderous Turkey)
The Abominable Dr. Phibes
I love City of Lost Children. It’s gleefully weird and full of beautiful visuals.
Did you mean “Forbidden Zone”, the Richard Elfman movie? If so, one of my all time favorites, and one of those movies that friends either ‘get’, and love, or hate and resent you for showing it to them.
Another little known weird movie: The Return of Captain Invincible. I describe it to people as, “It’s Alan Arkin as an alcoholic, washed-up superhero battling Christopher Lee. And it’s a musical.”
The same. Not sure why in my head it’s “Into the Forbidden Zone”.
I have only seen Wrong all the way through, but I am still confident in my choices.
Love Rubber, couldn’t get into Wrong, will have to try again but Wrong Cops looks aweseomez!
Koo! Koo! Koo!
The entire thing is freely and officially available (with English subtitles) on YouTube courtesy of Mosfilm:
There was also a recent animated remake. It’s not bad, but it doesn’t come anywhere near the gloriousness of the original.
Yet another: The 5000 Fingers of Dr. T. A live action movie created and written entirely by Dr. Seuss. Stars Tommy Rettig from Lassie and, most memorably, the wonderful Hans Conried. It looks and feels like a Dr. Seuss story. Utterly weird and worthwhile.
Caught a restored print of that one on the big screen when the kid was still youngish at SIFF. He was the perfect age for it then and it was great to see in the theater.
I love Eraserhead but I am weird so I don’t know xx
Not a single mention here of Seijun Suzuki? Branded to Kill is one of those movies that sounds perfectly normal when you describe the plot to someone — unsurprising, as the original script before it was reworked was for a fairly generic yakuza B-movie — but doesn’t do justice to the oddity of it.
(In some ways it reminds me of Repo-Man, in that at least one plot point was partially based around a company that they had received funding for product placement from.)
And no mention either of Guy Maddin? Admittedly, some of them work better if you know what movies he’s drawing his inspiration from (e.g. Tales from the Gimli Hospital is clearly drawing from German expressionism, Brand Upon Brain! from the early Surrealist films), but they’re still weird as hell.
I usually have a list of weird movies on my mind, where my criteria of “weird” changes with my mood. Now I am thinking of - in no particular order:
Death Powder
A Journey Into Bliss (Die Reise ins Glück)
Dandy Dust
Jumborg Ace and the Giant
Raspberry Reich (uncensored version)
Dr. Calgari
Phase IV
Ascension of the Demonoids, The Devil’s Cleavage, Sins of the Fleshapoids (pretty much anything from the Kuchar brothers)
On the Silver Globe (Na srebrnym globie)
Black Devil Doll from Hell
Brain 17
The Rider of the Skulls (El Charro de las Calaveras)
Demon Seed
Bad Biology
Reflections of Evil
Sixteen Tongues
Double Down
Mystics in Bali
The Boxer’s Omen
American Astronaut
Hanuman and the Five Kamen Riders
I will Walk Like a Crazy Horse (J’irai comme un cheval fou)
The Ninth Configuration
The Bed Sitting Room
Liquid Sky
The Arrival (and all other Unarius movies)
Shirley Pimple and The John Wayne Temple of Doom
Little Boy Blue - Tiny Terrestrial
Chosen Survivors
Ghosts That Still Walk
Shivers (They Came from Within)
Actium Maximus
I-Be Area
Wax - or, The Discovery of Television by the Bees
Faust (Jan Svankmajer version)
