Indy 500 The first racing game I ever played, we only had the demo I couldn't have been much older than 3 or 4, I remember crashing into walls blew the tyres up. It was probably the first game I ever played.
Skid marks This was a silly game, my older brother had it on his Amiga. I remember it because the computer asked you if you wanted to play. I also remember my older brother telling me that skid marks are poo marks in ones pants.
Toca 2 Touring Cars This was my first game on the Playstation. The game was so realistic, it was also really hard for me. My older brother more or less completed the game for me/himself. We used to play hide and seek, and tag on it. I also remember being excited when he unlocked the AC/Shelby Cobra.
These probably aren't my favourite racing games ever (Skid marks for example) but these were probably the most influencial.