Battou-Jutsu for Beginners
Kenjutsu is the prevalent martial art in the series, which should make sense, considering that the main character wields a sword - reversed-edge or not. Kenshin is a master of the art known as battou-jutsu, which earned him the name of Battousai. Battou-jutsu is often used interchangeably with iai-jutsu. However, according to some purists, iaijutsu places an emphasis on drawing the sword, cutting, and re-sheathing the sword - all in a single fluid movement. Kenshin's techniques are more about fast-drawing and cutting (often several times). Both place an importance on the first strike (in iai-jutsu, the only strike) immediately following the draw. Even though with a sharp sword and a strong arm, it can inevitably be a killing blow, the very essence of the sword art is to avoid conflict or to contain it. The practitioner aims to attain victory without ever drawing the sword and if the necessity to draw it arises, to not hesitate to do so. It was usually done in self defense or as a preemptive strike, which is why so much emphasis is placed in the series on Kenshin's (god-like) speed. There must be no opportunity for a counterattack. Once that's done, back into the scabbard the sword must go, the sheathing also being an important and dangerous part of the skill, as one may easily cut oneself with the blade. Unlike kenjutsu, the sword always starts sheathed in battou- and iai-jutsu. In older times, iaido, tournaments pitting one samurai against another in iaijutsu, were held to keep their instincts sharp. They were the equivalent of European jousts with lances, or Midwestern quick-draw duels among gunslingers. Even now, iaido is practised as a sport and discipline. Yahiko, Kaoru, Saitou, and most of the villians practice kenjutsu which don't typically place the same importance on the act of drawing. In fact, Yahiko and Kaoru's weapons are the shinai and bokken - which are not sheathed.
Kenshin's skills in battou-jutsu were so superior that he was able to demonstrate the "return cut." Using a daikon (giant radish), he was able to deliver a cut so fast and so accurate that no cells were damaged and the daikon halves were seamlessly reunited into a whole radish.
Some characters also practice kempo (or kenpo), such as Misao, Aoshi, Hanya, and - possibly - Anji. It's often used as a general term to refer to many forms of unarmed combat. I don't know if Sano qualifies as a kempoist since he's just an overstrong barroom brawler with very little regard for technique, focusing instead on raw strength.
Lastly, all of the Oniwabanshuu practice ninjutsu, which covers most ninja skills associated with stealth attacks, espionage, explosives, and other forms of, er, not-so-direct combat combined with more traditional weaponry.