I'm also starting off with a short list of films. I'll add the proper info later.

nos amours
L'Argent 

Berlin Alexanderplatz
Bird
Black Rain
Blue Velvet 
Born on the Fourth of July

A City of Sadness
Come and See

Days of Eclipse 
The Dead
The Decalogue
Do The Right Thing

The Elephant Man
L'Enfant secret

Fast Times at Ridgemont High

Hail Mary

Landscape in the Mist 
Love Streams

Paris, Texas
Pixote 
Platoon
Le Pont du Nord

Raging Bull 
Reds

The Sacrifice
Salvador 
Sans Soleil
sex, lies, and videotape
Shoah
Stranger Than Paradise
A Summer at Grandpa's 
El Sur

A Time to Live and a Time to Die

Under the Sun of Satan