Classic movies you feel deserve their classic status?

I agree with all of yours. Here are some of mine, all from the group sometimes called "The Film School Generation" (Spielberg, Scorsese, Lucas, Coppola):

The Godfather
The Godfather, Part II
Apocalypse Now
Close Encounters of the Third Kind
Jaws
Schindler's List
Star Wars
The Empire Strikes Back
Raiders of the Lost Ark
Taxi Driver
Goodfellas

Alien/Aliens
L.A. Confidential
Rocky
The Shawshank Redemption
Close Encounters of the Third Kind
The Thing
The Fifth Element

Gone With the Wind
Tale of Two Cities
Titanic
Some Like It Hot
The Day the Earth Stood Still
The Fly
The Thing
To Have and Not Have
The African Queen
Streetcar Named Desire
To Kill a Mockingbird
...to name a few

gone with wind

Metropolis
Battleship Potemkin
The Third Man
North by Northwest
Nosferatu
Yojimbo

My old faves:

"Quo vadis" (1951)
"Ben Hur" (1959)

Sunset Boulevard
Who's Afraid of Virginia Woolf

2001
Ben-hur
Citizen Kane
The Godfather
Gone With the Wind
Psycho