One of my favorite movies (and very underrated IMHO) is "Thirteen Days." It is about how the JFK administration handled the Cuban Missile Crisis with the Soviets in October 1962. The thumbnail sketch is that U.S. spyplanes photographed evidence that Cuba had offensive nuclear weapons, which posed a grave threat to America. Other than Kevin Costner playing JFK advisor Kenny O'Donnell, the film does not have a ton of big name actors. But it is well-written, shows the time period accurately, and is a gripping story of how close the U.S. came to a nuclear war with the Soviets.