Can't argue much with Alek's list, at least as far as historically influential directors go. Here's my alternate picks of personally influential directors, along with my favorite film from each one. Same rules as Alek.
George Melies, The Black Imp
Buster Keaton, Sherlock Jr.
Walt Disney (I know, not really a director, but...) Snow White and the Seven Dwarves
Jean Renoir, Le Grande Illusion
Ernst Lubitsch, To Be or Not To Be
Yasujiro Ozu, Ohayo
Vittorio De Sica, Bicycle Thieves
Francois Truffaut, Small Change
Jean-Pierre Melville, Le Cercle Rouge
Martin Ritt, The Spy Who Came in From the Cold
Andrei Tarkovsky, Stalker
Woody Allen, Annie Hall
James Ivory, A Room with a View