Pole Position, Atari 2600. Played that for quite a while before I realized the "pieces of a picket fence" that I was dodging around the track were actually other cars? I still have it, but both of my Atari's have a different problem with them. I wish I had the ability to put the two together and have one working one
Spy Hunter, NES. Not exactly a racing game, but definitely one of my favorite driving a car fast games. Top down view, blow up the "spies," drive into the back of a semi truck to upgrade your weapons/oil slicks/smoke screens. Great game, played the hell out of it.
Grand Turismo 2, PSX. My first racing "sim." Loved it, especially after I got a cheapo Mad Catz wheel. I loved how it was so... difficult. I could tell people, "it's not a game, it's a sim."

I played that game so much, it's ridiculous. I had a lot of fun with GT4 too, but that was short lived as I then found LFS.
Mario Kart also gets an honorable mention. Not only was it a mega-fun racing game, it was probably the best multiplayer console game I've ever played. That kept me up many many nights at friends' houses and stuff back in the day. *sigh*