The Beat 'em Up genre is a cousin to the Fighting Game genre that is popular today. Most games that fall under this genre have very little in the way of story, and lots in the way of bash-the-other-guy's-heads-in-with-your-fists action. Co-Op Multiplayer in these games is a highly popular feature.
These games eschew one-on-one duels for the protagonist (and a friend or two) rampaging across the map, handing out unmerciful beatdowns to every group of gangsters, mutants, robots and ninjas they meet, acquiring weapons from their environment and finding cooked chickensinexplicably hidden inside arcade cabinets.
Related to the Hack And Slash, a Beat 'em Up that primarily includes weapons and sometimes magic. Expect some cross-pollination.
In Japan, Beat 'em Ups of the Double Dragon or Final Fight variety are known as "belt-scroll" games due to their semi-isometric perspective and the fact that the characters are always facing left or right despite being able to move up and down as well. Games like Kung-Fu Master (which is completely side-scrolling) or Beat Down (which is in 3D) are not considered belt-scroll games.
Beat Down: Fists Of Vengeance, a dismal 2000s 3D Beat 'em Up from Capcom made to capitalize on Grand Theft Auto's success; Mainly remembered for the characters' liberal use of the F-word.
Fear Is Vigilance, A free 2D beat 'em up web-game about a pair of college students trying to get college students to pick up free personal alarms to keep them safe at night — by creating something for them to keep safe from.
Fighting Force: considered to be one of the earliest attempt at a 3D beat 'em up, was original developed to be a Streets of Rage sequel.
Ninja Baseball Bat Man, the general concept and initial designs were made in America with the intent of it being the follow-the-leader platformer game; It was sent to Japan for programming, and when it came back, it became "Power RangersWITH BASEBALL!".
Renegade (a.k.a. Nekketsu Kōha Kunio-kun), the first beat 'em up that used the "belt-scroll" perspective, which allowed characters to move along both the vertical and horizontal axis while still facing primarily to the left or right
The Punisher, a two-player arcade game by Capcom co-starring Nick Fury; Also released for the Genesis.
Sailor Moon had a few alongside the fighting and puzzle games; It can be very entertaining to see tiny girls like Mercury and Moon bust out DDTs and suplexes.
X-Men, a six-player arcade game by Konami loosely based on the "Pryde of the X-Men" animated pilot featuring Cyclops, Wolverine, Storm, Colossus, Nightcrawler, and Dazzler.
X Men Legends and its sequel, X-Men Legends: Rise of Apocalypse, as well as its spiritual successor series Marvel Ultimate Alliance, are more recent additions to the genre.