These codes are typed in at the stage select screen:

All Weapons:
Press C-Left, C-Down, C-Right, C-Up, Z, L, R, C-Left, C-Down, C-Right, C-Up.

All Levels:
Press C-Up, C-Right, C-Down,C-Left, R, L, Z, C-Up, C-Right, C-Down, C-Left.

GameShark Codes

Enable Code    f1192B80 2400
Infinite Life  8020A965 0064
Infinite EXP.  8020A967 00FF

Thanks to Revolution readers Crooky and Danny H!