Yet another game that starred Mario but somehow neglected to put his name in the title, the Japan-only Famicom Grand Prix: F-1 Race is one of the predecessors to Super Mario Kart. Though not nearly as advanced as the game that would follow it five years later, it was still fun. It was even followed by a sequel: Famicom Grand Prix 2: 3D Hot Rally, which also failed to mention that it starred Mario (and Luigi!).
Famicom Grand Prix: F-1 Race (1987)