I'm not gonna put them in order, and I am also going to include the first Driver game, as you only played in a vehicle, and you did race against the clock and in some missions the police. I'm also going to try and only include one game from franchises. Like, I could put Gran Turismo 1-3 in there easily, maybe even 4. But boooooooring.
Need for Speed III: Hot Pursuit. The PSone classic. Awesome SP experience, challenging AI.
Sega Rally Championship 2. On the Dreamcast, of course.
Gran Turismo 2. The pinnacle of the franchise imho.
Burnout: Takedown. Still might be the best MP racer I have ever played.
Rallisport Challenge 2. Amaaaaaaazing. If I were putting them in order this might be #2 behind GT2.
Daytona USA. The DC version was really good. The Saturn version, that framerate though.
Driver. Only the first one. Awesome driving, great physics, especially the exaggerated flying cop cars.
Destruction Derby: Raw. Much better than the other two games imho, and the N64 DD was crap. Instead of race cars and tracks with some demolition mixed in, these tracks were all about setting up awesome collisions.
World Driver Championship. An amazing and imho underrated N64 gem.
Forza 4. The pinnacle of the Forza franchise imho.