Carmageddon - You don't even need to drive fast in this game, just kill off your opponents and you win.

Death Rally - Incredible game.  Work you way up from the bottom to be the best.  Features a lot of cars and upgrades.

Grand Theft Auto - The first ever GTA was also good.  Complete missions, drive around town, or just see how many cops you can get chasing you.

Lotus 3 - The Ultimate Challenge - Choose from a multitude of options in this game.

Micro Machines 2: Turbo Tournament - Race a variety of vehicles in a miniature world.

Street Rod (a.k.a. Hot Rod) - Race others for money or pink slips. You can upgrade and buy/sell cars also.

Wacky Wheels - Race other animals as an animal in crazy little go carts.