Koopa the Quick

Koopa the Quick is a special Koopa found in Super Mario 64. They first appear in the second mission of Bob-omb Battlefield, and then a second and final time in Tiny-Huge Island. Upon being talked to, they will ask to race the player. Beating Koopa the Quick in a race to a flag with a Koopa shell on it will reward the player with a star.

Third Race
In some personalized copies, there is a third race with Koopa the Quick. This is usually the hardest race, and appears in copies that have raised difficulty. The location of the third race varies, though is occasionally in it's own small level.

Mouth
Interestingly, Koopa the Quick has a red polygon located inside his head, presumably to represent the inside of his mouth. However, his mouth never opens, even when he talks, so this red polygon goes unseen by the player in normal gameplay. There is no animation for his mouth opening, either, so this feature seems to have been scrapped early on.

Koopa the Slow
Koopa the Slow is the name given to an anomaly that can occur with Koopa the Quick that makes them incredibly slow, sometimes to the point it takes hours for them to reach their goal. This has caused the missions with Koopa the Quick to be effectively impossible without incredible patience. This anomaly is likely due to the Personalization A.I. trying to make Koopa the Quick easier to deal with and failing horribly and making it impossible in a much different way.