I'll just list some of my favorites, as there are thousands of films that fit the bill:

Ichi The Killer (2001 / Japan / Takashi Miike)
pretty demanding study of different modes of violence, at the same time reflecting and satirizing it, going against all viewer expectations regarding slasher films, heros, villains, etc.,etc. Demands several viewings - the most complex Miike film I've seen to date.

El Topo (1970 / Mexico / Alejandro Jodorowsky)
Surrealist denouncement of society and heroic concepts. Pretty moralizing.

Institute Benjamenta (1995 / UK / Brothers Quay)
Adaptation of a german novel by Robert Walser transported into "ber"-surreal Quay territory. Critique of society's hypocrisy.

Possession (1981 / West Germany, France / Andrzej Zulawski)
Best film I've seen so far on the devastating effect a @#%$ up relationship can have on your psyche. Zulawski supposedly made this after a three year divorce-hell he went through with a wife he still loved. The persons have deep psychoses' and the film is mostly filtered through their point of view, so be prepared for a very troubling film. (with gruesome "unintentional" abortion scene). A claustrophobic tour-de-force set against the cold-war in Berlin that doesn't give you room to breathe.

The Beast (1975 / France / Walerian Borowczyk)
Satire on church, society, and "morality" that doesn't leave anyone off the hook.

Goto, island of love (1968 / France / Walerian Borowczyk)
Imagine 1984 crossed with Kafka and populated by hillbillies. Devastating account of structural oppression resulting from ignorance. Everybody is basically oppressing himself in an enclosed society that has lost its humanity.

Woman in the dunes (1964 / Japan / Hiroshi Teshigahara)
Allegorical tale about the meaning of life. What is a human being when stripped of all possessions? What's important what isn't? Critique of modern-day society and a call for choosing your own fate. 

Stalker (1979 / Soviet Union / Andrei Tarkovski)
Same as above, but set in a distant "totalitarian" society that has destroyed its humanity. 

Diamonds of the night (1964 / Czechoslovakia / Jan Nemec)
Surrealist tale of two jews that have escaped from a train was deporting them. Critique of Czech fascists during WWII.

Daisies (1966 / Czechoslovakia / Very Chytilova)
Two girls try to break free from society's restrictions, but don't realize that they themselves are part of it. 

Branded to kill (1967 / Japan / Seijun Suzuki)
Suzuki playfully deconstructs the Yakuza "genre" and builds it up anew. 

Kuroneko (1967 / Japan / Kaneto Shindo)
Social critique packaged as a surreal horror-fable.

The Shining (1980 / USA / Stanley Kubrick)
Exploration of the aftereffects of slavery and the genocide of the indians on a society that doesn't want to aknowledge its past, packaged as a horror film. Also reflection about the correlation between photography and the film, image and reality.

Class relations (1984 / West Germany / Straub/Huillet)
Hommage to cinema, literature and the theater, and a critical account of the USA, through an adaptation of Franz Kafka's Amerika.

Angel's Egg (1985 / Japan / Mamoru Oshii)
Exploration of faith. Allegorical anime told in long takes with minimal dialogue. 

Lost Highway (1996 / USA / David Lynch)
A schizophrenic has murdered his wife, but doesn't want to aknowledge it. Told from his POV, you will get a mind-boggling display of images.

Lulu on the bridge (1998 / USA / Paul Auster)
Allegorical tale of the (im)possibility of love. Very melancholic.

Tokyo Decadence (1992 / Japan / Ryu Murakami)
One day in the life of a neurotic Tokyo prostitute who has lost her personality. But the people surrounding her are even worse of because opposed to her they don't even seem to have noticed this fact in their own lives. One day in soulless hell. Beware - highly depressing.

Three Days (1991 / Soviet Union / Sarunas Bartas)
Three people trying to find love in post socialist Russia. But do they even know what they are looking for? Isolation and apathy, almost completely without dialogues.

The Death of Stalinism in Bohemia (1990 / UK / Jan Svankmajer)
Svankmajer reflects on 40 years of dictatorship, but in his usual surrealist way. Agit-prop at its best.

I married a strange person (1997 / USA / Bill Plympton)
Crude satire on love and death in the US. 

Faust (1994 / Czech Republic / Jan Svankmajer)
surrealist re-telling of the Faust saga.

The reflecting skin, and Salo also recommended.