Published by Nintendo for the Super Nintendo Entertainment System. The first racing game released for the SNES, which made extensive use of the on-board graphics hardware. You race one of four cars around a series of tracks. Five laps make up a race. Each lap has a "LIMIT"; if your car finishes the lap ranked worse than the maximum limit, the race ends. If you have a spare machine left, you can retry the race. The same goes if you crash (run out of power) or give up.
An unofficial (?) sequel, F-Zero 2, is circulating in ROM circles. However, it does not add any significant gameplay features, such as multiplayer. It merely replaces the cars with cooler-looking sprites and adds some wacky new tracks. (This is based on the ROM that I have, which may or may not be related to BS F-Zero 2. BS F-Zero 2 was released for the Satellaview system in Japan only.)
Followed officially by F-Zero X for Nintendo 64, F-Zero: Maximum Velocity for Game Boy Advance, and F-Zero GX for GameCube.