Just saw this for the first time in years and it still holds up well. I think the most impressive thing is the subtle sense of foreboding which builds and builds throughout. The only film that comes to mind like that is Miracle Mile, which is also about the end of the world funnily enough. Can anyone recommend others with that same mood?
You might try Let the Right One In, or its American remake, Let Me In. They are a completely different genre, but they both have an undying sense of foreboding.
If you want to go back half a century, I'd recommend On the Beach (but treat the remake as if it were radioactive), or The Andromeda Strain (again, avoid the remake like the plague).
To get a little closer to the genre, try Slaughterhouse-Five (there's no remake, so you won't need to jump around in time to find the best version).
There's also The Lathe of Heaven, a great movie with terrible production values (it was made for about 20 grand in 1980). You might recognize a younger Senator Kelly from X-Men (or an older Willard) as the main character. But the remake, Lathe of Heaven (no "The"), is a nightmare (pun intended) so don't see that one.
For a lighthearted comedy that has a driving sense of dread, look for Steven Spielberg's feature film debut, The Sugarland Express.
Naked by Mike Leigh. Brilliant movie starring David Thewlis. Basically just follows a sadist around as he runs into one bizarre character after another and messes with people's heads. It's very unsettling but also highly entertaining because they mix in a lot of dark humor. Just a very creative, unusual and interesting film.