Motorstorm Arctic Edge is an amazing PSP racing game. Lots of race events and a variety of vehicles to choose from. The game is also one of the best looking games on PSP IMO. Another great arcade style racer is Ridge Racer. The game is especially enjoyable if you're a fan of the older games like Ridge Racer Type 4.
If you want something more racing sim-like, then Gran Turismo is good, but lacks a career mode from the console versions. I personally didnt have as much fun playing this as the above mentioned games, but it does look nice and has a pretty good assortment of tracks and cars.
Motorstorm looks pretty sweet. To go a little off topic here, there are so many good PSP games at what I'd consider to be dirt cheap prices! Now I don't even know of a racing game is the way to go. --- PSN: ImpulseDOM- http://img94.imageshack.us/img94/6136/ev9ngy.gif
Wipeout Pulse. I love the Wipeout series. It's fast and ranges from easy to extremely challenging depending what difficulty you play on. I find the series extremely addictive too. It's one of those games that will keep you up at night. --- ~Nintendo 64. Get N or Get out. Coming Fall 1996~