I guess I have to say it would be one of the following, assuming "classic" to be prior to 1970?

To Kill a Mockingbird
All Quiet on the Western Front
Anatomy of a Murder
In the Heat of the Night
Dr. Strangelove


Runners up include:

Spartacus
Key Largo
The Third Man
Casablanca
The Seventh Seale
12 Angry Men
Citizen Kane
Space Odysey 2001
Yojimbo as a double with Fistfull of Dollars