Beat em up is a term commonly applied to
action games where the action derives from
beating up computer opponents. Classic games in this
genre would include
Double Dragon and the original
arcade version of
Teenage Mutant Ninja Turtles.
Capcom and Konami provided most of the excellent arcade beat-em-up's from the 80's and 90's, including the Simpsons (arcade) Sunset Riders, Cadillacs and Dinosaurs, and Dungeons and Dragons: Tower of Doom. The NES cult classic River City Ransom is another example of at beat-em-up.
The beat-em-up as a genre is slowly dying. With the introduction of fighting games like Street Fighter II, arcade and home gamers alike had their attentions focused on a new enemy other than "the computer": their fellow humans.
Street Fighter clones in 2-d and 3-d now command a big chunk of the floor space in arcades, and while games like Die Hard Arcade and Zombie Revenge attempt to bring the beat-em-up into 3-d, the future for the genre looks fairly bleak.