UFO
Hold [R1] + [R2] + [L1] + [L2] at the car selection screen and choose a car. Keep those buttons held and press [X] at the transmission selection screen. Then, hold [Triangle] until the race begins.

Alternate car colors
Press [Square] at the car selection screen.

Reversed tracks
Complete circuit mode to unlock an option for forward and reversed tracks.

Stunt mode
Complete tournament mode to access a stunt mode option on the Golden Gate track.

All cars
Press [Triangle], [Square]x2, [X], [R1] at the options screen. A sound will confirm correct code entry.

Truck
Select any car, then hold [L1] until the race begins.

Buggy
Select any car, then hold [R1] until the race begins.

Hidden car
Select any car, then hold [R1] + [R2] until the race begins.

Various cars
Select any car, then press [Down] at the transmission selection screen to cycle between a low rider, bus, rocket engine car, taxi, and police car. Note: The number of cars that are selectable will vary depending on how many keys have been found. To drive the police car, circuit mode must be completed.

Additionally, press [Circle] at the car selection screen to access four more vehicles, including a Viper, hippy van, VW Beetle, and McClaren.