Enter the following at the title screen:

Bottomless canteen 
Hold L + R and press Left, X, B, Down, X, A, X, B 

Classic Pitfall game 
Hold L + R and press B, B, Left, Right, B, X, A, Up, B 

Hyper punch mode
Hold L + R and press Left, Right, B, Up, B, Right, Left 

Play as Nicole
Hold L + R and press LEFT,UP,DOWN,UP,B,UP,UP 

Classic Pitfall mini-game: 
Hold L + R and press B(2), Left, Right, B, X, A, Up, B at the title screen. 
The "Original Pitfall" option will be unlocked at the "New Game/Load Game" 
screen. 

Classic Pitfall 2: Lost Caverns mini-game:
Buy all items from the Shamans and collect all Idols.