Road Rash by EA, originally released on the Sega Genesis in 1991.
I have to say, looking for images on a Google Search about a game called "Road Rash" leads to some pretty disgusting results. Do yourself a favor and avoid this, unless you happen to work in a meat kitchen and are desensitized..
Road Rash was one of EA's early efforts on the Sega 16-bit system, back in the day when they were considered fairly rogue (they started out releasing their own carts unlicensed on the unit, before becoming buddy-buddy). Lots of the games they released often stood in stark contrast to the mostly-Japanese-produced stuff that filled out the stocks otherwise, for better or worse (usually the latter). But you had to give EA some credit for trying to forge their own path, with often interesting (if imperfect) product.
Road Rash represented a period when the quality of those games started to step-up, considerably. The only previous (notable) motorcycle racer to appear on the system was Sega's own Hang-On, which was a fun (if choppy) arcade port. Road Rash showed up and showed that game up quite a bit, with much smoother and impressive scaling graphics, and more to do.
The game puts you in the boots of a lone racer, driving across the California freeways. You are racing for money, which can be used to buy enhanced equipment. The big deal here was that you could attack other racers (punching or clubbing them), "fighting dirty" as they call it. It was a refreshing experience unlike any which had been attempted on the system before.
Road Rash wasn't without its' issues: the framerate felt a bit skippy, the colors were rather grainy, and the handling was a bit loose. But overall this was a fun (if unconventional) racer which went on to be a successful and respected franchise, for some years.