The best kind of games I loved playing in the arcades were the ones where you walked through streets and other settings beating people up using fists, feet, and weapons

Burning Fight, Combatribes, The Double Dragon series

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Growl, Knights of the Round, Knuckle Bash

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Final Fight, Ninja Combat, Captain Commando

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Punisher, Alien V Predator, Sengoku

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Silent Dragon, Superman, Undercover Cops

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Crime Fighters, 4 player beat em up.. incredible game. Once you finish the game you get to re-fight all the bad guys one at a time (timer then another comes out and another, if you dont defeat one, they pile up quick).

If you get to finish that the game throws all the bosses at you at once. Ever single stinking one of them. A friend and I finished it in the arcade even past this zone to have our names immortalized until they got rid of the game. We even had a crowd that rivalled some crap tables.