Growing up on a PS2 which had a game library that consisted of NOTHING BUT driving games here's my list for you:
Gran Turismo 3 and 4, if you're into racing simulators.
The very first Stuntman was a great arcade driver. The Sequel, Stuntman: Ignition was a disappointment, though.
Need for Speed: Hot Pursuit 2 was a great arcade-simulator with police chases and all that good stuff in exotic Supercars.
And Finally, the burnout series was a really fun arcade racing game with spectacular crash effects. Burnout 3 being the all-time best of the series.