Quirky
Amélie
The City of Lost Children - Jean-Pierre Jeunet and Marc Caro, 1995
Les Triplettes De Belleville
Creature Comforts
Delicatessen
Pee-Wee's Big Adventure
Edward Scissorhands
Time Bandits - Terry Gilliam, 1981
The Adventures of Baron von Munchausen - 1988
After Hours - Martin Scorsese, US 1985
Something Wild

Happy
Double Happiness - Mina Shum, 1995 (Hong Kong?)
The Wedding Banquet - Ang Lee, 1993
Eat Drink Man Woman - Ang Lee, 1994 Taiwan
Celestial Clockwork - France/Venezuela/Spain/Belgium, 1995

Comedy
Spinal Tap
Best in Show
Waiting for Guffman
Planes, Trains and Automobiles
A Fish Called Wanda
The Big Lebowski - Cohen Brothers
Fast Times at Ridgemont High
Almost Famous

Dark Comedy
Cold Comfort Farm - John Schlesinger, UK 1996
Happiness - Todd Soldov
The Cook, the Thief, His Wife and Her Lover - Peter Greenaway, France/UK 1990
Lolita - Stanley Kubrick, US 1962
There's also a new version starring Jeremy Irons which is good, but not as good as the Kubrick one. The original has Peter Sellers.

Serious, emotional and beautiful
Blue - Kieslowski, Krzysztof France/Switzerland/Poland, 1994
White - Kieslowski, Krzysztof France/Switzerland/Poland, 1994
Red - Kieslowski, Krzysztof France/Switzerland/Poland, 1994
Breaking the Waves - Lars Von Trier, Denmark/France, 1996
Vukovar - Boro Draskovic, Yugoslavia 1994
About the war in Serbia
Ponette - Jacques Doillon, France 1996
Not much dialogue. A very young girl (5?) is the star in this movie and she is a brilliant actress. Sentimental, rather sad but a good ending.

Drama
Lord of the Rings Series
Amateur - Hal Hartley 1994
The Unbelievable Truth - Hal Hartley
Trust
Smoke
Kiss of the Spider Woman
Sling Blade - Billy Bob Thornton
Lone Star - John Sayles
Men With Guns - John Sayles
Hotel Rwanda
The Man Who Wasn't There - Cohen Brothers
Lamerica - Gianni Amelio, Albania 1995
The Last Emperor - Bernardo Bertolucci, Italy/China 1987
Europa Europa - Agnieszka Holland, France/Germany/Poland 1991
The Sweet Hereafter - Atom Egoyan, Canada, 1997
Cinema Paradiso - Giuseppe Tornatore Italy,1988
Secrets and Lies - Mike Leigh, 1997

Adventure
Until the end of the World - Wim Wenders, 1991

Romantic Comedy
The Princess Bride

Romance
Il Postino - Michael Radford, France/Italy 1994
Pride and Prejudice (2005)

Action
Snatch - Guy Ritchie, UK 1998
Fight Club

Mystery
Music Box - Costa Gavras, 1989
The Vanishing (Dutch title is "Spoorloos") - George Sluizer, 1988
There is also a Hollywood version, but it's probably crap. Get the foreign one. It's very creepy. This is the one you should rent for Halloween if you can find it.
Silence of the Lambs

Turn of the Century
Angels and Insects - Philip Haas, 1996
The Age of Innocene - Martin Scorcese, 1993
Sense and Sensibility - Ang Lee, UK 1995
Wings of the Dove - Iain Softley, UK 1997