Crash Bandicoot 3 Demo:
At the "Press Start" screen, press L1 and Triangle to see the demo.

Level Select:
During play, pause and go to the Inventory screen. Now press Square, Square, Circle, Square, Left, Right, Left, Right, Circle, Up, Right, Down. When you go to the Ballonist, you'll have access to all levels.

99 Lives:
Press Square, Square, Square, Square, Square, Square, Circle, Up, Circle, Left, Circle, Right, Circle.