Too many games to list... my thoughts are Mortal Kombat or a wrestling game.
The only beat each other up games that I played mostly was:
Mortal Kombat ... all of them (SNES) & PC
Clayfighter 2 (SNES)
Tekken (Playstation)
Seen other people play the wrestlemania games but those aren't my thing. Use to watch wrestling on TV in the 1980s as a kid/teenager, but its so fake. I prefer something more violent i guess which mortal kombat and clayfighter 2 were, with clayfighter being non gory.
I play mostly dungeon crawlers, rpg & mmorpg, fps, adventure and puzzle games like tomb raider and myst, and car racing games.