Film student 101:Battleship Potemkin
Kieslowski's Trois Couleurs
Schindler's List
Akira Kurosawa's films
A Clockwork Orange
Wong Kar Wai's films (I suggest "In the Mood for Love" and "Chungking Express")
The Breakfast Club
The Seventh Seal
Pedro Almodovar (check out "Volver" and "Todo Sobre Mi Madre")
Kill Bill 1 & 2
Pulp Fiction
Sin City
Miyazaki cartoons
As for my actual favorites, I'll list them by genre:
Comedy/Musical:Everyone Says I Love You (Woody Allen)
Purple Rose of Cairo (Woody Allen)
Mary Poppins
About a Boy
High Fidelity (as a rule most Nick Hornby adaptations are ace)
Garden State
The Royal Tenenbaums (Wes Anderson)
Clerks (Kevin Smith)
Mallrats (Kevin Smith)
The Concierge/For Love or Money
Ferris Bueller's Day Out
Roxanne
Father of the Bride
The Jerk
The Man with Two Brains
Grease
Fantasy/Suspense/Sci-fi/Horror:Army of Darkness
Tremors
The Innocents (I've not seen this actually, but the concept is interesting.)
Dracula (Gary Oldman/ Winona Ryder)
Labyrinth (Jim Henson)
The Dark Crystal (Jim Henson)
Dark City (Alex Proyas)
I, Robot (Alex Proyas)
Bicentennial Man
The Others
The Sixth Sense
Shaun of the Dead
Total Recall
Drama/RomanceGreat Expectations (Cuaron)
Much Ado About Nothing (Branagh)
Chasing Amy (Kevin Smith)
Before Sunrise (Richard Linklater)
Before Sunset (Richard Linklater)
Almost Famous (Cameron Crowe)
Tortilla Soup (adapted from Ang Lee's Eat Drink Man Woman)
My Sassy Girl (Korean film)
Windstruck (Korean Film)
One Night Stand
Three of Hearts
Me And You And Everyone We Know
Higher Learning
The Joy Luck Club (adapted from the Amy Tan novel)
St. Elmo's Fire
Little Manhattan
Animation/ Children's:An American Tail
Spirited Away (Hayao Miyazaki)
Pom Poko (Hayao Miyazaki)
Waking Life (Richard Linklater)
Ratatouille
Aladdin
Beauty and the Beast
Mulan
Triplets of Belleville
Tokyo Godfathers
Cats Don't Dance
The Last Unicorn
The Little Princess (Alfonso Cuaron)
Action/War:Hudson Hawk
Casualties of War
Yeah. That's a lot but believe me, there's a lot more where that came from.