Okay, this could take a while. To begin with, don't bother with Saito's group, or Angs, or Kevin's. Without invoking this sites fraudbusting rules, there is no reason for you to even consider these groups if you are after anything even closely related to Ninjutsu or Japans Ninja. Okay? Cool.
Now to the fun stuff.
Tenshin Shoden Katori Shinto Ryu is one of the most respected and oldest Koryu in Japan (Koryu are the old systems, predating the Meiji Restoration of 1862). It was founded (according to tradition) in 1447 by Iizasa Choi-sai Ienao (he took the name Choi-sai later in life, a not uncommon practice. Takamatsu Sensei was known by a number of names, originally being born Hidetsuna, and taking Toshitsugu later, Hatsumi's original pronunciation of his given name was Yoshiaki, later Masaaki, Tanemura was originally Tanemura Tsunehisa, later Tanemura Shoto). Iizasa was a highly skilled practitioner of a number of existing systems at the time, including being the 7th head of the Muso Jikiden Ryu Yawaragi (Jujutsu), and practicing a sword art known as hitotsu no tachi, or the solitary sword.
According to the tradition, Iizasa spent 1000 days training and meditating at the sacred Katori Shrine (both the Katori Shrine and it's related Kashima Shrine were near to where he was stationed) at the age of 60, and afterwards, while he slept, the Guardian Deity of the Katori Shrine, Futsunushi no Mikoto appeared to him in a dream, and presented Iizasa with a scroll detailing the secret principles of swordsmanship, called the Mokuroku Heiho no Shinsho. With this newly acquired knowledge, Iizasa went on to found the Tenshin Shoden Katori Shinto Ryu (The School of the Heavenly True and Correctly Transmitted Style of the Katori Shrine).
The main focus of the school is Kenjutsu, but being a Sogo Bujutsu, or composite martial system, it also encompasses many other weapons and teachings, including Bojutsu, Naginatajutsu, Sojutsu (spear), Kodachijutsu (short sword), Ryotojutsu (two swords), Shurikenjutsu (spike throwing), Yawaragi (jujutsu), Iaijutsu (sword drawing), and more esoteric forms of knowledge such as battlefield tactics, castle fortification, spiritual teachings, and ninjutsu, which in the Katori Shinto Ryu refers to methods of espionage.
A major aspect of it's approach to it's training (which is entirely in kata form, predominantly paired, except for the Iai, which is solo) is based on a revolutionary concept (in it's day, at least). In the kata, which could be made up of up to 20 movements on each side, Iizasa utilised a method in which the Uke-Tachi (recieving sword partner) would substitute his sword for the particular body part the Shidachi was striking to. So what often appears to outsiders as a blocking action is really a device employed to allow the combat to continue, and to allow the partners to experience full contact, restisted blows safely with relatively heavy wooden weapons (even more important when dealing with items such as Naginata).
The school has been a major influence on many other systems over the centuries, including systems such as Shinto Muso Ryu Jojutsu, the founder of which, Muso Gonnosuke, said to be the only person ever to defeat the legendary Musashi in a duel (although that story is only recorded in some versions of the Shinto Muso Ryu histories), was a Menkyo Kaiden (full mastership licence) holder in Katori Shinto Ryu, and the related Kashima Shinryu. It has also produced some of the greatest swordsman in Japans history, probably none more famous or skilled than Bokuden Tsukehara, founder of Shinto Ryu Kenjutsu.
Katori Shinto Ryu has continued to be passed down over the last 500+ years within the same herditary line, with the current Soke being Iizasa Yasusada, the 20th Head of the Ryu. Due to health reasons, he is not able to be the head instructor for the Ryu, and has authorised Otake Risuke as Shihanke, or Head Technical Teacher for the system. In the Ryu proper, only those who have a link to Otake Sensei are considered a part of the Ryu itself, and therefore studying the art.
In order to join the school, you are required to take Keppan, which is a blood oath, invoking the wrath of the Katori and Kahsima deities should you break your vows. There were originally 4 rules that were adhered to without variation, but the last three have been more relaxed in recent times, leading to a raise in popularity. The rules were:
1: Admittance in restricted to those prepared to take Keppan and pay the associated Dojo fees.
2: Foreign students must reside in Japan.
3: Upon leaving Japan, foreign students must not teach the art in any way.
4: If learning Katori Shinto Ryu, no other martial arts may be practiced.
One of the very first foreign students was Donn Draeger, also Menkyo Kaiden in Shinto Muso Ryu, and he was responsible for popularising the art. He studied under Otake Sensei.
There is another branch of the Ryu, though, known as the Sugino-ha. The Sugino Dojo didn't enforce these rules, nor require Keppan to be taken, so it has spread further faster, and is more accessible to more students around the world.
This has lead to a bit of controversy, as under the authority of the Soke, Otake Sensei authorised Sugino Yoshio as an Instructor within the Ryu, however Sugino Shihan died in 1998, and his students are not connected with Otake Sensei or Iizasa Soke. This technically means they are not a part of the Ryu itself, and are therefore by definition not able to claim to be studying the art, even though Sugino Shihan's son has taken over the mantle of Dojocho for his fathers school, and they teach the exact same curriculum (with only tiny differences, such as the Otake line having their hips more square-on than the Sugino-ha, and the weapons in the Sugino Dojo-lines being a timy bit smaller due to Sugino's slightly smaller stature than Otake's). Sugino Sensei was also an incredibly highly skilled practitioner, and served as a technical advisor and fight choreographer for Kurosawa's films "The Seven Samurai", "The Hidden Fortress", and a few others.
The group in WA is linked to the Sugino Dojo in Japan.
This is probably one of the best, if not the best, Koryu videos I have ever seen.
(Follow the links for parts 2 through to 4, it's definately worth it!).
It features Otake Shihan going through the majority of the Tenshin Shoden Katori Shinto Ryu's Omote Kata, or the "outer" techniques. Without the actual instruction by someone who really knows these kata, you will never actually get what the lessons are, and these are also only the "outer" techniques, or the public face of the art. This is what is shown to the general public, the "true" system is kept for initiates only.
Okay, that was a bit off-topic, I know, but if you are interested in history, and interested in the Japanese Martial Traditions, you really do need to know about TSKSR. It's almost blasphemous to not do so....