Sega really used to focus on game quality back in the day.
Adding additional moves and tons of areas to beat up some baddies, Streets of Rage to is an epic game that can be as relaxing or intense as you want it to, with music to match. The four character control differently and offer unique experiences. Some players will feel more comfortable knowing that there may be a character that matches their play style.
Add in great boss battles, detailed cities and towns, tons of moves, object use, and smarter enemies and you have yourself one of the top beat em ups made.
A game you will not want to miss. apparently it is also available for modern gamers on XBL, not sure how well that one plays, but give it a try if you don't have a Genesis or can't buy it off Ebay!