Famicom Grand Prix: F-1 Race
October 30, 1987
The pilot is shown on the game's cover to be Mario. In the game itself he's only shown before the start of the race, and after winning it. An oddity is that also the other pilots look like Mario.
Super Mario Bros. Game & Watch special edition
A special edition of the Super Mario Bros. Game & Watch, in a case shaped like the Famicom Disk System mascot Diskun, was given out as prize for a Famicom Grand Prix: F-1 Race tournament.
F-1 Race (Game Boy)
November 9, 1990
After winnning each course, a Nintendo character shows up to greet the pilot, right before the start of the next course. The Mario ones are (see F-1 Race cameos for other series):
Copyrights for both series are held by Nintendo.