Three semi-random suggestions: Pi, Cypher and One Point O.
All are mysterious sci-fi flicks.
I haven't seen Primer, but I suspect it fits in with these movies.
Finally I found someone who thinks too that Cypher is a great movie.
I try to keep it short, but I recommend:
Nolan movies (mainly Memento, Inception and Prestige, ... see them all)
Fincher movies (mainly Fight Club, Se7en, The Game, Benjamin Button, Social Network, ... see them all)
Pixar movies (mainly Finding Nemo, Wall-E)
Kaufman movies (mainly Eternal Sunshine of the Spotless Mind, Adaptation)
Gilliam movies (mainly 12 Monkeys, Brazil, The Fisher King)
Hitchcock movies (mainly Spellbound, Psycho, Rebecca, Rope, The Man Who Knew Too Much, The Birds, ... too tired to write them all out)
Iñárritu movies (mainly Babel, 21 Grams, Amores Perros)
Tykwer movies (mainly Lola rennt, The Parfume)
Coen movies (mainly the comedies: Untolerable Cruelty, O Brother where are thou, Big Lebowski, but the dramas are good too)
Natali movies (mainly Cube, Cypher, Nothing)
Aronofsky movies (mainly Pi, Requiem for a Dream, The Wrestler) haven't seen Black Swan yet
Movies with Edward Norton (mainly Fight Club, Primal Fear, American History X, The 25th Hour) haven't seen Moonrise Kingdom yet
Other movies by Genre:
SciFi: Scott Pilgrim vs. the World (2010), Cloverfield (2008), Children of Men (2006), Donnie Darko (2001), Frequency (2000), Abre los ojos (1997)
Drama: American Beauty (1999), Magnolia (1999), Time of Awakening (1990)
Music Drama: August Rush (2007), Once (2006), La leggenda del pianista sull'oceano (1998)
Romance: The Notebook (2004)
Crime/Thriller: Brick (2005), The Machinist (2004), Gosford Park (2001), The Usual Suspects (1995)
Comedy: Stranger than Fiction (2006), Garden State (2004)
Older ones, by year, see them all:
Paris, Texas (1984)
Network (1976)
2001: A Space Odyssey (1968)
Once upon a Time in the West (1968)
Breakfast at Tiffany's (1961)
The Appartement (1960)
Witness for Prosecution (1957)
12 Angry Men (1957)
The Night of the Hunter (1955)
Le salaire de la peur (1953)
Dark Passage (1947)
Citizen Kane (1941)
Maltese Falcon (1941)
M (1931)
I stop here, I think now you have something to do...