Drive a sheep
Defeat all opponents in "School" mode. Then select "School" mode free trial. Hold Select + Circle before entering the Zero 4 (1-1) course to use the Sheep.
All courses
At "Push Start Button", press and hold X + Select + Circle + Start. Keep pressing and press Up + L2. Keep pressing all buttons and press Square.
All Cars
At the title screen, press and hold L1 + L2 + R1 + R2. Keep pressing and press Up + Triangle. Keep pressing all buttons and press Start.