Who are your favorite directors, and what do you think their best film is?

For me...
1. Alfred Hitchcock - Strangers on a Train
2. Steven Spielberg - Jaws
3. Peter Weir - The Truman Show
4. Sidney Lumet - 12 Angry Men
5. Martin Scorsese - Taxi Driver

Martin Scorsese - Goodfellas
Spike Lee - Do The Right Thing/25th Hour (tie)
Steven Spielberg - E.T.
Robert Zemeckis - Forrest Gump
Tim Burton - Batman/Sleepy Hallow (tie)
Kasi Lemmons - Eve's Bayou
Mario Van Peebles - New Jack City
John McTiernan - The Hunt For Red October
John Landis - Trading Places/Coming To America (tie because CTA is my favorite movie)
Clint Eastwood - Mystic River

John Hughes - The Breakfast Club/16 Candles
Peter Jackson - Lord of the Rings Triology
Alfred Hitchcock - The Birds/Psycho
Stanley Kubrick - Full Metal Jacket
James Cameron - Titanic
Ang Lee - Brokeback Mountain
Steven Spielberg - Saving Private Ryan
Spike Lee - Summer of Sam
Tim Burton - Edward Scissorhands
John Carpenter - Halloween
Francis Ford Coppola - The Godfather
Sam Raimi - The Evil Dead
Brian DePalma - Carrie/Dressed to Kill
Clint Eastwood - Gran Torino
Mel Gibson - The Passion of the Christ
George Romero - Night of the Living Dead
Sean S. Cunningham - Friday the 13th 1, 2, 3

Mel Gibson - Apocalypto
Quentin Tarantino - This is tough as hell, but I'ma go with Jackie Brown/Inglorious Bastards for the tie.
Ron Howard - A Beautiful Mind

There are just too many good Directors and their movies to restrict to 10.

These are in no particular order...
Ridley Scott - Alien
James Cameron - Aliens
David Fincher - Se7en
Steven Spielberg - Raiders Of The Lost Ark
Quentin Tarantino - Pulp Fiction
Martin Scorsese - Goodfellas
Guillermo Del Toro - Pan's Labyrinth
John Carpenter - Halloween
John McTiernan - Die Hard
Peter Jackson - LOTR

James Cameron - Titanic
Christopher Nolan - The Dark Knight
Victor Flemming - Gone With The Wind
Steven Spielberg - Jurassic Park
Tim Burton - Edward Scissorhands
Wes Craven - A Nightmare On Elm Street

Akira Kurosawa-Seven Samurai
Federico Fellini-Nights of Cabiria
Werner Herzog-Aguirre, Wrath of God
Fritz Lang-M
Alfred Hitchcock-Rear Window
Martin Scorsese-Taxi Driver
Jean Renoir-Grand Illusion
Francis Coppola-Apocalypse Now
John Cassavettes-Husbands
Francois Truffaut-Jules and Jim
Andrei Tarkovsky-Andrei Rublev
John Ford-Stagecoach
M. Antonioni-L'Avventura
Wim Wenders-Wings of Desire
Ingmar Bergman-Persona
Stanley Kubrick-2001: A Space Odyssey
Orson Welles-Touch of Evil
Quentin Tarantino-Pulp Fiction
Howard Hawks-Red River
Coleman Francis-The Beast of Yucca Flats

I could go on...