Recently I started wondering about the possible origin of the techniques i.e. where did Rumiko Takahashi get the ideas for them from. Here is my theory on some of them:
Kachü Tenshin Amaguriken and the Bakusai Tenketsu are quite likely based on and possibly a tribute to Hakuto Shin Ken (Fist of the North Star). The techniques are very similar and Tetsuo Hara (creator of Fist of the North Star) and Takahashi were colleagues at Kazuo Koike's art school. Though the Breaking point should by this reasoning work the way Ryoga thought it would and blow the opponent up.
Martial Arts Cheerleading techniques are based on the fighting style of the Sun Wukong (known better as the Monkey King) seen in the Chinese epic novel Journey to the West. One of the bystandards even makes a comment about this (though in the VIZ version the comment was changed to be a reference to Dragon Ball Z which is also based on the Monkey King). Primarily the extending baton and the many pompoms resembling a cloud.
Anything Goes Martial arts is at least partially based on Bruce Lee's Jeet Kune Do since in an interview Takahashi stated that she used to watch Bruce Lee movies specifically stating Enter the Dragon in an interview in Animerica.
Jackie Chan early movies are likely a large influence on the fighting style as well. Quote from interview: "I used to watch a lot of Jackie Chan movies. There is also, of course, Bruce Lee and Enter the Dragon" Ranma's using anything like paper fan and pinwheels as weapons are likely based on early Jackie Chan movies. One particular style seen in the manga is definitely based on his movies. During the Romeo and Juliet arc girl form Ranma gets drunk and uses Drunken martial arts which is quite likely based on Jackie Chan's movie Drunken Master.
Ranma's sitting style (hanging on walls, sitting upside down) and comments (insults in battle) are likely based on Spiderman who Takahashi said in an interview (Amazing Hero's 1990) that she really liked during her junior highschool years (also that she collects the comic Animerica Vol. 9 No. 6). Lucky (Happosai's friend) has a technique where he mixed ink with glue that had a similar effect to Spiderman's webbing.
Ninjitsu is also seen by several characters. Ranma for instance uses trading place with an object technique several times, used a smoke screen to get Miss Hinako away from some boys while she was unconscious, etc.. Multibody technique is seen by Konatsu.
Kuno's style is Kendo.
Basically Ranma's fighting style is likely a mix of Jeet Kune Do, Ninjitsu, spiderman style, Jackie Chan movie style, and a bit of Fist of the North Star.