Adam Hunter was a police officer in a city rampant with crime and corruption, perpetuated by a secret criminal syndicate. When Adam and his colleagues Axel and Blaze couldn't convince their superiors to take up arms against the syndicate, they quit the force and took to the streets as vigilantes to bring down the criminal organization themselves. This scenario serves as the plot of the first Streets of Rage games.
Despite the unlikelihood of bringing down a powerful organization that had wormed its way into every echelon of power in a city's local government by traversing the streets and punching people in the face , the three vigilantes were successful in their endeavor, even defeating the enigmatic head of the syndicate, Mr. X. Adam returned to the police force afterward, while Axel and Blaze took up other employment.
Adam was absent as a playable character in the game's sequel however, as he was attacked and taken captive by a rejuvenated Syndicate a year after the events of the first game. His younger brother, Eddie (who bears the unfortunate nickname "Skate") took his place as a playable character as he, Axel, Blaze and Max (a wrestling buddy of Axel's) took to the streets once more to destroy the syndicate and save Adam.
Suffice to say, they were successful in this and while Adam wasn't beaten or abducted by the third game he didn't return as a selectable character. Instead, he remained as a supporting character, providing the others with information, and occasionally more active assistance in the form of a helicopter.
An older Adam makes his triumphant return as a playable character in Streets of Rage 4. He is a specialty officer now, rooting out corruption in the force. Adam now has a teenage daughter, Cherry. Adam is unlockable approximately half-way through the game, and his SoR1 version is also unlockable.