Monkey Jockey
At the main menu hold in the L3 button and quickly press Up (2), Left, Right (2), Down, Circle Square. When you start a game, a monkey will be riding on the horse.
Konami / Nintendo Snake Jockeys
At the main menu hold in the R3 button and quickly press Down (2), Left, Right (2), Up, Circle Circle. When you start a game, likenesses of Hideo Kojima (creator of Metal Gear) and Shigeru Miyamoto (Super Mario creator) will be riding snakes. This is an injoke because the two collaborated on the GameCube version of Metal Gear Solid: The Twin Snakes.
Horse Riding Jockey
At the main menu hold in the R3 button and quickly press Up (2), Left, Right (2), Down, Circle Circle. When you start a game, the horse will be riding on the back of the jockey. Note: It is almost impossible to win a race as the jockey can't run very fast due to a horse being on his back.