Alex Kidd in Shinobi World was originally just going to be a cutesy spin-off of Shinobi called Shinobi Kid, but Alex was shoe-horned in so he could piggy-back off the popularity of Shinobi as his own license was on the out.
The PS2 Shinobi was originally planned as a Dreamcast game, but the intended platform changed due to Sega's abrupt departure from the hardware race.
Shinobi III was initially titled The Revenge of Shinobi II and featured entirely different levels and enemies. Apparently, the mediocre reception this iteration got from several gaming magazines led to Sega scrapping it and overhauling the game. You can read about it here.