Purely influential films are (in my opinion)

Birth of A Nation (like it or not, Griffith was a genius)
Citizen Kane (inspired more filmmakers than any other film)
A Bout De Souffle
Stagecoach (set the principles of every modern western)
2001: A Space Oddyssey
Battleship Potemkin (still the greatest editing ever)
Psycho
City Lights (any Chaplin film really)
La Dolce Vita
Jaws (changed movies forever by being the 1st blockbuster)
Taxi Driver
Seven Samurai (Coppola and Lucas idolized Kurosawa)
The Seventh Seal
Faces (Cassavetes is the godhead of independent film)
The Apartment (wait...a film can be funny and sad?!??)
La Regle De Jeu 
The Godfather
Bringing up Baby (the granddaddy of screwball comedies)
The 400 Blows
The General (Keaton was the greatest)
Metropolis (1926)
The Maltese Falcon (the first detective noir)
Annie Hall
Un Chien Andalou
Trouble in Paradise (the father of sophistication in movies
was Lubitsch.)