My favorite racing games are the Mario Kart series and that one game... uh I think it was called Beetle Adventure Racing or something like that. That was a good racing game too. Mario Kart is known by many, so I don't think I need to explain that one.
Beetle Adventure Racing took the Volkswagen Beetle and gave it power-ups and other things to make it more fun I guess. I also have played some of the Need for Speed games, but only the second one I think. I thought that was a pretty good game as well.
Other than that, I am not really a fan of the racing genre. I don't actively seek out such games, and when given a choice, I prefer adventure or platformers.