So much of this depends on your personal taste. That said, no one should leave this earth without seeing 'Casablanca' (and, for the record, had it been me the world go stuff itself, I'd run off with Ingrid Bergman.)
Here are three that have yet to be mentioned.
One of the black and white Alfred Hitchcock movies. There are many good choices, but I'd go with 'Notorious' (Bergman again, so maybe I'm biased.)
The Grapes of Wrath--director John Ford has to be on any list
The Philadelphia Story--funny and touching.
I cannot believe anyone has not mentioned SUNSET BOULEVARD???!!!
"I am big. It's the pictures that got small".
Her bed is reason enough to watch it.
Narcissism, sadism and psychosis at it's finest.
The Day the Earth Stood Still
The Defiant Ones
12 Angry Men
They still have a knob on the telie that removes the colour and revert the set to B&W?
1. The Bishop's wife - with Cary Grant
2. A Night to Remember - sinking of the Titanic made in the 50's
Abbott & Costello Meet Frankenstein
Casablanca
Wizard of Oz
The Quiet Man, Sunset Blvd, Young Frankenstein, Topper, Gaslight, Mrs. Miniver