There are so many films about apocalypse and the aftermath that there are websites devoted just to them. If this interests you, try http://www.apocalypticmovies.com/ which is attempting to build the largest database of such films. Unfortunately, this is not a genre I like, so I can only recommend a few classics. Like science-fiction films, these movies often deal with challenging and thoughtful issues, so I regret my lack of enthusiasm for them.

When Worlds Collide: 1951 by Rudolph Mate. A planet is on a collision course with the Earth, and no will listen to the warnings.

The Day the Earth Stood Still: 1951 film by Robert Wise, recounting the results of the arrival of an alien spaceship.

On the Beach: 1959 by Stanley Kramer, a classic post nuclear tale in which the last survivors deal with the knowledge that they have only a few days to live.

Planet of the Apes and Beneath the Planet of the Apes: 1968 and 1970 respectively, by Ted Post. A spaceship crashes on an Earth-like planet that is run by intelligent apes. Very clever.

Independence Day: 1996, by Roland Emmerich. Planet Earth is invaded by hostile aliens and scientists struggle to find a defense.