These are outliers from the mainstream, so I'll list them first.
For strange old art film, Belladonna of Sadness is a sad but good pick~
Cool new art film and hilarity of human condition, Mindgame!
Typical stuff:
The films of Satoshi Kon (Paprika, Tokyo Godfathers, Perfect Blue, Millennium Actress, etc)
Studio Ghibli films and shorts
OVAs by Gainax from their early era (Gunbuster and Diebuster)
The short film collections of Studio 4 degrees C
Though not anime, short films from graduates of the French animation school
Gobelins are amazing.