The PS2 version of Hot Pursuit 2 is fun, as CyborgGT recommended. It's the only version of that game worth playing (the Xbox/GCN/PC versions were made by a different development team). I would also recommend Midnight Club 2 and/or 3, Outrun 2006, Burnout 2 and/or 3, and Ridge Racer V. I never had any fun with the TOCA series -- GRID was the first game I considered worth a purchase.
If you're okay with plunking down money on quirky, flawed Japanese racing games with unique car selections and race locations, there's also the Tokyo Xtreme Racer series. TXR Zero and TXR3 offer Wangan-Midnight-style hijinks on the Tokyo highway system, while Tokyo Xtreme Racer Drift 2, which orimarc mentioned, offers drift competitions and races on remote Japanese mountain roads. If that sounds cool, go for it, but I'll warn you, the physics in these games are barely playable.
If you like motorcycles or would be interested in learning about them, there's also PD's own Tourist Trophy, though it's more of a riding game than a racing game, similar to Gran Turismo. For ultimate realism, though, Suzuki TT Superbikes is as close as it gets (on the PS2 anyway).