Infinite Health:
During play, press White, Black, White, Black, Y, Y, Y, Y, B, B.

Show Objects:
During play, press White, Black, White, Black, Y, Y, B, X, X, B, R, R.

Aquarang, elemental boomerangs, dive and swim skills:
During play, press White, Black, White, Black, Y, Y, X, X, Y, X.

Technorangs:
During play, press White, Black, White, Black, Y, Y, Y, X, Y, X.

Unlock Gallery:
During play, press White, Black, White, Black, Y, Y, A, A, R, X, R, X.

Unlock Best Ending:
Beat the game with all cogs, eggs, and opals for 100% to unlock a bonus stage, extra FMV after the credits, and a new option in the extras.

Thanks to Revolution readers Poo[SGL] and GamerDude!