This was the first game I bought for my game cube, and it is still the one I play the most. Here are the reasons:
The graphics are great. The tracks are very realistic, since they are made from actual places near San Francisco (I'm pretty sure that's the city)
Unlike other racing games, Burnout encourages you to drive badly and to have accidents! Driving on the wrong side of the road and doing other dangerous things earn you points, which can be used to activate the "turbo" power. And when accidents occur, they are really great and realistic. There is even a game mode where you have to start the biggest accident possible.
There is a great selection of cars, from SUV to police car (complete with siren) to racing car. And the best part is, there is a horn on all of them which can be activated to get other cars out of the way!
Multiplayer, championship, single race, and even a pursuit mode where you have to chase and hit your "target" car with a police car.
I think if you want a fun city racing game, Burnout is the one to get. It's great, except for the music. But that's a minor detail.