Films that deal with memory, identity, reality with drugs, time travel and body-swapping. In fact, movies that will make you question your sanity and/or that of everyone you come into contact with.
There are some on the list who appear again and again, so you can be sure that most films by Lynch, Jodorowsky, Cronenberg, Gilliam, Greenaway and Anger are worth tracking down for their strangeness, as are adaptations of works by people like Philip K. Dick.
This list came about from my search for the weirdest films, granted there are surrealist films on here but the bulk come from filmmakers going out and making the films they want to make. Without too close an eye on them from the studios and with apparently little regard for the audience's tastes (or sanity) they can sometimes hit moments of truly transcendental madness that can be better than drugs (or at the very least similar). Where you get that sudden suspicion that you might have gone mad and what you are seeing on the screen is really being projected from inside your head.
See also: crazy horror films, weird Japanese films, crazy kung fu horror films and time travel films.
The removed: Weird porn films that'd cause problem with the list: Baby Sitter, Sinful Dwarf, Ginger's Sex Asylum and Angel Above - The Devil Below. Hypertrophy Genitals Girl is currently not listed here.