Ok, here is my list (some of them already mentioned), especially recommended titles are in bold:
Animation:
Coraline
Adventures of Mark Twain
Les Maîtres du temps (if you can find it)
Ice Age 1
Toy Story 3
Monsters, Inc.
Shrek 1-2
Aladdin
The Simpsons
Jamie and the Magic Torch
Japanese anime:
Howl's Moving Castle
Spirited Away
Kiki's Delivery Service
My Neighbor Totoro
Death Note (!!!)
Serial Experiments: Lain (!!!)
Neon Genesis Evangelion
The Last Exile
The Twelve Kingdoms
Haibane Renamei
Mushishi
Fairy tales/adventures:
Stardust (!!!)
Grimm
Bridge to Terabithia
The Goonies
Superheroes:
X-Men
The Incredible Family
Spider Man (episode 3 is best)
Torrente (!!!)
Potentially disturbing but deeply moving films:
Der Untergang (aka Downfall, Hitler's Last Days)
La Haine (Hate)
The Wrestler
Dogville
Dancer in the Dark
Eyes Wide Shut (this one goes deeeeep)
Mindfuck (sort of)::
Fight Club
Memento
Revolver
ExistenZ
Pi
Beautiful and touching tales on human existence:
American Beauty
K-Pax
most movies of Hal Hartley (like Amateur, Trust or Simple Men)
The Double Life of Veronique and the "Three Colors" trilogy by Krzysztof Kieslowski
Wings of Desire (and its sequel, Far Away So Close) by Wim Wenders
Le Fabuleux Destin d'Amélie Poulain
Cinema Paradiso (one of my all-time favorites)
Gran Torino
Love Actually (I think very highly of this film)
About Schmidt
Movies with a mystical/paranormal bent:
The Prestige (!!!)
The Time Traveler's Wife
The Devil's Advocate
Sixth Sense
Flatliners
The Others
Ink
Time travel:
Frequency
Back to the Future
Immortality:
Highlander (only the first one)
No words, just gorgeous pictures and music:
Koyaanisqatsi
Powaqqatsi
Baraka
Drug culture:
Traffic
Blow
Human Traffic
Comedy:
Groundhog Day
Crna mačka, beli mačor
Se til venstre, der er en svensker (this one is hilarious if you are in the mood)
Dr. Strangelove
Men in Black 1
Sitcom:
IT Crowd (first season + first episode of season 2)
Spaced (esp. because of Brian and his artistic endeavors)
Big Bang Theory
Weeds (only the first two seasons)
Science fiction (sort of):
Terminator 2
12 monkeys
Alien
Avatar
Total Recall
Starship Troopers
13th Floor
District 9
E.T.
Equilibrium
Contact
Matrix ( esp. the third episode
)
Star Wars IV-VI (as you see, this is an all-inclusive list)
Blade Runner (!!!)
Martial arts:
House of Flying Daggers
Crouching Tiger, Hidden Dragon
Space:
2001: Space Odyssey
Solaris (the Soderbergh version)
Goa/trance related:
Welcome to Wonderland
Liquid Crystal Vision
The Wonderland Experience
Apocalyptic documentaries about a possible bleak future:
Age of Stupid
Collapse
...and a documentary on a beautiful planet that we can lose if we don't get our thing together:
Home
Concert films:
Dead Can Dance: Toward The Within (!!!!!!!!!)
Pink Floyd: Live at Pompei
...and the rest:
Ghetto Millionaire
Kontroll
Moulin Rouge
The Beach
Point Break
True Lies
A History of Violence
Eastern Promises
Twin Peaks (the whole series, this is a masterpiece)
99 francs (by Jan Kounen)
Other worlds (documentary on ayahuasca shamanism, also by Jan Kounen - director of Blueberry/Renegade)
The Big Blue
Leon
Nikita
Titanic
Truman Show
Waking Life
The Fountain