In that case:

Musicals:
Singin in the rain
Bathing beauty
GiGi
etc.

Jesus, guys, let's not be retarded. Movies have been around since the late 1900's. Movies from the 80's and 90's are not old.

Here's my list of good, actually old, films:

Year, Name, Director
27 The General Buster Keaton
31 Frankenstein James Whale
31 M Fritz Lang
33 Duck Soup Leo McCarey
35 Bride of Frankenstein James Whale
38 Bringing Up Baby Howard Hawks
39 Stage Coach John Ford
40 His Girl Friday Howard Hawks
43 Shadow of a Doubt Alfred Hitchcock
44 Double Indemnity Billy Wilder
47 Out of the Past Jacques Torneur
48 Red River Howard Hawks
48 Treasure of the Sierra Madre John Huston
49 Criss Cross Robert Siodmak
49 The Set-Up Robert Wise
50 Rashomon Akira Kurosawa
50 Ace in the Hole Billy Wilder
51 On Dangerous Ground Nicholas Ray
53 Wages of Fear Henri Georges Cluzot
54 Rear Window Alfred Hitchcock
54 Seven Samurai Akira Kurosawa
55 Kiss Me Deadly Robert Alrich
55 Night of the Hunter Charles Laughton
56 The Killing Stanley Kubrick
57 Sweet Smell of Success Alexander Mackendrick
59 North by Northwest Alfred Hitchcock
59 Some Like it Hot Billy Wilder
60 Psycho Alfred Hitchcock
62 Lawrence of Arabia David Lean
62 Cape Fear J. Lee Thompson
63 The Birds Alfred Hitchcock
64 Dr Strangelove Stanley Kubrick

In the 60's, the power of many of the old giant movie studios was broken up, and a lot of more unusual and individual movies started appearing.

Some American films tried to be more like European ones. Bonnie and Clyde was influenced by the French, and old-fashioned Hollywood westerns were shaken up by Italian "spaghetti" westerns.

I'd classify these films as the end of 'old' movies and the birth of modern ones.

66 The Good, the Bad, and the Ugly Sergio Leone
67 Bonnie and Clyde Arthur Penn
68 Planet of the Apes Franklin J. Schaffner
68 Roseemary's Baby Roman Polanski
68 2001: A Space Odyssey Stanley Kubrick
68 Night of the Living Dead George A. Romero
69 Butch Cassidy and the Sundance Kid George Roy Hill
69 The Wild Bunch Sam Peckinpah
69 Midnight Cowboy John Schlesinger