Shinobi III : Return of the Ninja Master

Invincibility

Choose the "S.E." selection on the options menu. Press B to play the "He Runs", "Japonesque", "Shinobi Walk", "Sakura", and "Getufu" songs (in that order).

Unlimited weapons

Set the "Shurikens" selection on the options menu to 0. Set the "Sounds" option to "Shuriken". Highlight the "Shurikens" option again and the 0 will change into the symbol for infinity.

Bonus points

Complete a level without throwing any shurikens to receive a 30,000 point bonus.