Fighting games

Fighting games are covering the hand to hand fight and close combat games.

Beat them up

This is mostly a 1Vs1 fighting game. Yet more exotic variant may occur such as IK+ which is 1vs1vs1 game.

Examples include :

Barbarian (from Palace software, violent beheading sword fights)
Panza kick boxing (obvious)
IK+ (Karate)
Budokan (mixed asian martial arts, armed or un-armed)
Karateka (obviously)
Uchi-Mata (Judo)

Beat them all

This is mostly a Player vs many enemies configurations, often involving scrolling through levels and levels Boss, and saving a sexy girl before she gets raped or even worse.

Examples include :

Double dragon
Kung-Fu master
Dragon ninja

This subgenre is often mixed with other styles and includes same mechanics such as platformers or shooters games.

Displays

This can be 2D (plateform-like) despite graphics having a deepth feeling.

Dragon ninja
Kung-Fu Master

Or pseudo 3D, mostly using horizontal yet Isometric/Oblique backgrounds

Renegade series
Double dragon
WWF superstars

Multi player

Of course such game is better with a multiplayer option.

Beat them up often involve Player1 vs Player2 multiplayer mode.

Beat them all often involve a co-operative Players Vs environment multiplayer mode.

Break it all

Rampage is some sort of this.

This games allowed 3 players modes, the aim was to destroy buildings, survive, eat soldiers and destroy Army vehicules.

Also this game allowed players to fight each others while doing all those things in a MonsterRumble way.

Video