Brazil!
David Cronenbergs Crash
Visitor Q and Gozu...
Tideland
Welcome to the Dollhouse has been a favorite since I was a kid, and since I'm on a Todd Solondz note... Happiness is the only movie that I've ever had to pause and take a breather from, it is an astonishingly wonderful film, just really intensely disturbing on several levels.
Class of Nuke Em' High Part 2! (another childhood favorite, yea I know not a kids movie, I think USA's Up All Night is responsible for this one, yay Rhonda Shears!)
Wild At Heart and Blue Velvet (Lynch in general)
Cube is twisted and very enjoyable
Salò o le 120 giornate di Sodoma, yea... I saw this one mentioned and I wanted to add a +1 (+5,000,000 to be perfectly honest)
Mysterious Skin, I'm on the fence on weather this film is twisted, or if it's just disturbing. It's really good regardless.
Through a Glass Darkly, again I'm not sure if it's twisted per say, it is however beautiful, and definitely is not conventional. I figured it was worth a mention here based on that.
I'll stop here, if I don't I'll really start rambling on and that would be bad.