Nintendo's Mario Kart series games are the most prominent Super Mario racing games. As of 2015, the most recent releases in this series are Mario Kart 7 for the Nintendo 3DS and Mario Kart 8 for the Nintendo Wii U. Featured Arcade Mario Kart titles are mostly limited to Japan.
While a quick Google search will show many non-Mario Kart Mario racing games, these games do not have permission to use Nintendo's copyrighted mascot and are therefore illegal. Namco made a deal with Nintendo to develop the Mario Kart arcade titles, clearly establishing their legality alongside those that Nintendo produces.