Crash Bandicoot 3:
Warped

Spyro The Dragon demo:
Press Up(2), Down(2), Left, Right, Left, Right, Square at the title screen.

Hot Coco bonus level:
Go to Level 14 and ride about half way through the level to find Alien crossing sign on the left hand side. Run into the sign to be transported to level 31.

Eggipus Rex bonus level:
Go to Level 11 and take the yellow gem ride. Continue until reaching the area where the huge dinosaur chases Crash. Allow the second pterodactyl capture Crash to reach level 32. 

105% completion:
Collect all relics and gems, including those from the Hot Coco and Eggipus Rex bonus levels. The relics that are collected must be at least gold or platinum. Then, approach Crash's sister, next to the save spot, to find another clear gem. Take the gem to view a very nice fireworks display and finish with a 105% completion status.

Instant Uka Uka (Pal version):
Press Triangle + Circle + X + Square. Note: This may only be done once per life.

Hint: Five lives location:
Begin game play on level 11 and take the yellow gem ride. Go All the way to the end, and use a double jump over the yellow gem. Then, use a double jump to cross over the steel wall to find five lives.