12. DR. STRANGELOVE

Let's forgo the political issues and the fact that it's satire, because I know other people and writers could do a better job of covering that (here are a few examples: http://www.filmsite.org/drst.html, Lindley, Roger Ebert.)
Instead, let's discuss the way this film is crafted.

We have three connected stories, each with life and death stakes, each taking place over a short period of time (with a "ticking clock") and in few locations.

In other words, it could easily be a Roger Corman film.

This movie was designed like a low-budget exploitation film. And there's a practical reason for this: movies on war and politics don't usually do very at the box office. Sure, a movie that glorifies war does, and a movie that has surface-level politics but is actually a thriller does, but movies that actually condemn the madness that is our geopolitics (in this case, the utter insanity of the Cold War) have not and do not.

Story one: General Jack D. Ripper gives an attack order to one of his base's aircraft.
Story two: the code is received and carried out.
Story three: another General briefs the President in The War Room about the unauthorized attack, and the fact that they are unable to stop it.

We cut back and forth as these stories escalate: an underling trying to retrieve the recall code, a suicide, the reveal of a "Doomsday Device", an attempt to restore the damaged bomb bays before the bomb goes off. In each scenario, we are dealing with life or death situations, primal urges.

So, if you want to make a movie about war (that doesn't glorify combat) or politics, make sure you can do it on a low budget. And if it's funny, even better.