Here are the teams/groups that appear in the manga/anime. For Uruha, I split them up into their small teams, but they are all part of Uruha or Ura Uruha. This page is not 100% because I have not finished the manga yet.
Team Hokage is lead by Recca Hanabishi and they were officially given the title during the Urabutosatsujin. The name was chosen out of respect for Recca and Kagero's lost clan. Team Hokage entered the tournament in order to protect Yanagi who would have been mercilessly hunted if they refused.
The three brothers that were sent to attack Recca and his friends after they escaped Kurei's mansion. The brothers attacked Yanagi, only to hurt Kagero instead when she got in the way of the attack in order to save Yanagi. Angry, Recca easily defeats them.
Team Ku is lead by Kukai, and is a well known group of fighters that are the most feared murderers in the northeast. Kukai and Saicho are the best known members of the group. The reason Team Ku entered the death tournament was to clear the name of the Ku martial arts school that got a bad reputation because of some members becoming killers for hire.
Circus got it's name by each member taking a character from their name and combining it with
the others. Circus, led by Yashiro, were a strong group that had made it to the semi-finals
in the previous tournament, only to lose badly against Uruha Kurenai. Resulting in the
death of their teammate, Karin. They entered the new tournament for revenge, but the
tournament proved much tougher than before. In each fight another of their members died
until only the leader was left. With no other choice, Yashiro forfeit. Passing his team's hope
for revenge to Team Hokage.
Uruha Maboroshi, led by Genjuro of the Jyushinshu, is a team that is made up of human chimeras of different levels (beast, plant). All results of Genjuro's experimentations with implanting madogu into the human body. Team Uruha Maboroshi was Hokage's first Uruha opponents in the tournament.
Uruha Oto, led by Neon of the Jyushinshu, and is made up of just her and her two little sisters. Uruha Oto specializes in the use of sound and excels at teamwork. Uruha Oto was Team Hokage's second fight with an Uruha team.
Uruha Rai is a one-man team made up of only Raiha of the Jyushinshu. Raiha, unlike his fellow Uruha members, does not believe in needless killing. Raiha always fought fairly, never cheating. Raiha is a ninja that uses a katana and normal skills rather than using his Madogu. When it came time to fight against Uruha Kurenai, Raiha held back and eventually forfeit during the first fight because he didn't want to hurt Kurei's chances of getting to the finals by killing his teammates, Which turned out to be a relief to Uruha Kurenai's members that knew of Raiha's skill.
Uruha Kurogane, lead by Jisho of the Jyushinshu, is a team not much is known about. Only one fight was shown, which was their fight with Uruha Ma that ended in the killing of all members, including Jisho, by Uruha Ma's leader. The names of Uruha Kurogane's other three members were never given.
Uruha Ma, lead by Magensha of the Jyushinshu, didn't have any specialty as all members had their own style of fighting. Uruha Ma showed their brutality when Magensha single-handedly killed their fellow Uruha members from Uruha Kurogane. During their fight with Team Hokage all members of Uruha Ma, with the exception of Magensha, began to respect Team Hokage. The respect was mutual, resulting in a strange friendship after the tournament.
Uruha Kurenai, lead by Kurei, was named after the woman Kurei had been in love with until she was killed by Koran Mori right in front of him. Uruha Kurenai was the most brutal of all the Uruha teams. It was Uruha Kurenai that killed Circus' member, Karin, resulting in their quest for revenge. Team Hokage had the most problems fighting Uruha Kurenai out of all the Uruha teams and many dark secrets were revealed, including a shocking truth for Team Hokage's Tokiya Mikagami.
The Jyushinshu were a group of Uruha's most powerful members that follow the orders of Kurei. Most members of the Jyushinshu were, and still are, loyal to Kurei.
Ura Uruha was a group made up of some of Kurei's Uruha, even members of the Jyushinshu like Magensha, that were acting as spies for Koran Mori. Whenever Kurei got the chance he would kill as many as possible. Some however, like Gashakura, returned to Kurei's side in the fight against Koran Mori.
After Kurei was freed from Koran Mori's control, Kurei brought together his most loyal members of the Jyushinshu together and named themselves Uruha Hokage as a sign of respect to Kurei's old clan that was ruthlessly destroyed 400 year ago. Uruha Hokage's only goal is to kill Koran Mori. Each member of Uruha Hokage has respect for Team Hokage, though this respect is shown differently by each member.
Uruha Shishiten is made up of the four most powerful members of Ura Uruha, easily more powerful than Kurei's Jyushinshu. Even Raiha, who had been hinted at being stronger than Kurei, showed a little fear around the Shishiten member, Aoi.