Makoto Shishio - Mugenjin
This sword is the brother of the reverse-blade sword(sakabatou). It is very special because it has a finely toothed edge on the entire length of the blade. Makoto Shishio wields this sword, and it is the very reason of his Homura Dama technique. This sword has taken the lives of so many people that each andevery time shishio slaye another person, traces of their body fat and oil were caught on the edge. When heat from friction is made by the sword, it ignites the substances on fire.
Himura Kenshin - Sakabatou
This is the reverse-blade sword that the rurouni kenshin carries on his belt. It is ideal for a rurouni because it cannot slay anyone. The blade is on the opposite side unlike the traditional japanese sword. There were 2 types of this sword made by Shakku Arai, the principal sword was given to kenhin by shakku' son, and the second was cut in half by Soujiro the Tenken. This sword defies the meaning of kenjutsu, killing one so that another can live.
Seta Soujiro - Kikuichimonji Norimonei
This is the sword used by Soujiro the tenken in his battle with kenshin at shishio's hiedeout of the six shrines. In their first duel, the sword got a small crack and was rendered useless. Later in the fight, soujiro's Shun Ten Satsu technique ended up shattering the sword into pieces.
Aoshi Shinomori - Kodachi
Shinomori Aoshi uses a kodachi in his first battle with kenshin. Later he results to using double kodachi's because Kodachi Nitou Ryu is much stronger than Kempo. A kodachi is a sword in between the length of a dagger, and katana(normal size sword). It is not very close from a wakizashi, in fact their pretty much congruent in size, but a kodachi is straight.
Zanza or Sanosuke - Zanbattou
The zanbattou is a giant sword that was oiginally made to slay a horse and its rider in combat, but later it had no use because no one could wield it because of its extreme weight. Sanosuke easily mastered this weapon, but kenshin cut in it in half in their first battle. Later in the manga he staples it back together.