Kenka Bancho. It's a series of japanese games for the PSP, with only the 3rd game being officially translated and released outside Japan as Kenka Bancho Badass Rumble. It's like playing a typical shonen anime set in high school, you're a delinquent who fights everyone from the other schools in order to become the ultimate badass. It's semi open world and you can beat pedestrians and innocent civilians, which reduce your badass meter, because real badasses only fight people who can fight back! And with their bare hands, weapons are for weak pussies! It's over the top and fun as hell. I've only ever met one other person mention that game, and it was an RPG friend of mine, when he bought a PSP for himself.

Something I highly recommend for anyone that enjoyed River City Ransom or similar beat'em ups.