Are there any 80's movies like this one?

One film that never gets mentioned in these types of lists, is the French film Les derniers jours du monde (2009)
http://www.imdb.com/title/tt1390405/reference
It's an end of the world story, but also a road-movie. Highly recommend.

"The Quiet Earth". Very different story, but still has some similar themes/vibes.

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After Hours, for the same “all-in-one-night” feel and frantic-ness of the main character.

Terminator, for similar atmosphere and “guy trying to stop an imminent threat but no one believes him” premise

Fight Club, especially the end with the running through the city and buildings exploding.