Grand Turismo 3: A-Spec
Gran Turismo 3 A-spec is a racing simulator. Players can race around detailed environments in popular cars such as the Toyota GT1, Panoz GT1 and Mazda 787B. A-spec gives players the opportunity to race in a variety of cups that feature only select cars (eg. '80s cars or roadsters). There is no online support, but A-spec does support two players splitscreen and up to six if you have an "iLink" (which allows you to connect multiple PS2s).
ATV Offroad Fury 3
ATV Offroad Fury 3 is a fast paced all-terrain-vehicle-themed racing game. With an emphasis on speed, high jumps and powersliding, Offroad Fury 3 offers something completely different from Grand Turismo. Progressing through the game's single-player mode will earn players credits that can be used to unlock new gear, clothing, and tracks. Up to six players are supported for online races, while the offline splitscreen component only supports four players.
Burnout 3: Takedown
Burnout 3: Takedown is a fast-paced racing game that rewards destruction and encourages crashing. Every high-speed crash is followed by a replay that can be manipulated to show the crash from additional angles. No licensed cars are available, but it's not hard to match the lookalikes to the cars they are modeled after. Two player splitscreen is supported, along with up to eight players online.