Race as a UFO: At the car-select screen, simultaneously press and hold R1, R2, L1, and L2 and pick your car. While holding the buttons, go to the transmission screen and pick your transmission, then press and hold g until the race begins. When the race starts, you'll be in control of a UFO.
Race as a Pickup Truck: Select your car, then simultaneously press and hold L1 and L2 until the race begins. When the race starts, you'll be driving a pickup truck.
Race as a European Car: Select your car, then simultaneously press and hold R1 and R2 until the race begins. When the race starts, you'll be driving a European car.