Infinite shruikens
This handy cheat will give you an infinite supply of Joe's main form of attack, and it is simply done in the same way as it was in The Revenge of Shinobi -simply change the amount of shruikens to "00" and then wait for it to change to a "∞", although unlike in the game just mentioned you only have to wait for about a second for it to change. Start the game and the shruikens will always be at "999".
Player 2 pad activated cheats
Player 2's controller will open up a host of cheats you can use during gameplay. Try any button for the following effect:
Start: Freezes game, music will continue to play, no pause menu appears, press again to unfreeze.
A: Press to move the game forward by just one frame at a time, only works when the game is frozen.
B: Skip the current section of the level you are on and start at the next.
C: Moon-jump, press rapidly to make Joe float. It also toggles if your weapons are powered-up or not.
Character/memory/map editors
Press A, B and C at the same time to go into the character editor. In this menu you can change the palette of objects and view them. Press start to go into the memory (mem.) editor, which lets you changed digits and bytes. Finally, you can press start again to enter the level editor (MAP mode), which allows you to move around the level and view it, allowing you too see parts you usually cannot. You can also place tiles you have selected by pressing the C button. Press start and B together to exit the editor screens. Naturally, a while manner of bizarre things can occur if you mess around with things in the editor screens, so experiment. Iceknight has been kind enough to let me put up his guide to these editors, view it here.