reanimator, highlander, mad max, blue thunder, nighthawks, punisher (with dolph lundgren), masters of the universe, World War III, Nico, death before dishonor
Red Dawn (WOOOLVEREEEEEEEEEEEEENEEEEESSSSSSSSSSS!!)
And already mentioned earlier in this thread:
The Last Starfighter (video gamer saves the galaxy FTW!!!)
Buckaroo Banzai and the (whatever) dimension (had a catchy tune)
They Live ("I'm here to kick ass and chew bubblegum, and I'm all out of gum)
Commando!! (lay off some steam, Bennett)
Hilarious movie from 1984 about a fictitious rock band touring America. The actors, Michael McKean, Christopher Guest and Harry Shearer do all the singing and instrument playing. A "must see" for any music fan.
I'm sure a bunch of the films listed in this thread weren't cult classics either - The Goonies still has a cult like following, and its full of epicness so imo - it counts as worthy of mention