I've been looking for some old films to watch online and I'm looking at
On The Beach (1959)
Patton (1970)
The Great Escape (1963)
The Guns of Navarone (1961)
Those last two inspired parts of the video game series, Metal Gear Solid. In Metal Gear Solid 3, a lot of films get mentioned by characters throughout the game.
On The Beach is one I heard about because Alex Jones was talking about nuclear war earlier this year, and he showed a scene from that particular film. There's a newer version of On The Beach but I'd always go for the original, or better, read the novel it's based on.