The Haunted Mansion

Invincibility
Hold Right, then push B, X, X, X, B, X, Y, A.
(Thanks to snumble_go@yahoo.com)

Level select
Hold Right, then push X, X, B, Y, Y, B, X, A.
(Thanks to snumble_go@yahoo.com)

Play as Invisible Zeke
Hold A + B + L + R at the opening sequence, before the legal screen. Release the buttons at the title screen.
(Thanks to snumble_go@yahoo.com)

Play as Skeleton Zeke
Hold A + B + X + Y at the opening sequence, before the legal screen. Release the buttons at the title screen.
(Thanks to snumble_go@yahoo.com)

Restore health
Save and quit your game. Then load your saved game, and you'll begin at the save point with full health.
(Thanks to snumble_go@yahoo.com)

Weapon upgrade
Hold Right, then push B, B, Y, Y, X, X, X, A.
(Thanks to snumble_go@yahoo.com)