In Ninja Assassin, the main character's name is Raizo, which looked familiar to us. A trip to IMDB gave us the answer: the actor Raizo Ichikawa was famous for a series of classic Japanese ninja movies, like Shinobi No Mono.
Shinobi no Mono is a complex, shadowy film, about two ninja tribes competing to kill off warlord Nobunaga. Ichikawa is an upcoming ninja in one clan, but he messes with the master's wife, so he must undertake some dangerous and dishonorable missions. Sent to Edo, he drops out of the ninja business and finds love with an innocent bargirl. But this happiness cannot last.
The movie has the beautiful look of Japanese B&W films, especially the day-for-night (or night-for-night?). There is a good deal less magical ninja stuff than you might hope - the ninja villages look pretty much like any village, except there is an explosives lab in a hut outside the walls, and the houses have some secret compartments. The action is pretty subdued by modern standards, but at least there's no magic leaps to the roof, and so forth.
I'm not sure if this is required viewing for lovers of the ninja canon, but it is suggested viewing for lovers of the samurai genre. Try it and see.