The Akatsuki Teams are put together in teams of two to exploit combined strengths for the Organization's goals to be met. Each team is lead by a senior member of the Organization. Each member of a team seem to have similarities with each other.
Active
Pain/Konan
Senior: Pain
Similarity: This team has three similarities.
Divinity titles (God for Pain; Angel for Konan)
Childhood Friends
Not trusted by Madara
Target: Nine-Tailed Demon Fox
A team that so far, functions very well with each other, evident that Konan is the only member to refer to Pain by name. As the leader of Akatsuki, Pain directs the rest of the organization to their respective goals, his most direct interaction with the organization is using the Illusionary Dragon Nine Consuming Seals. Pain is the leader of Amegakure, and has sense been referred to as a god there. Konan for doing her duties to Pain has been declared God's Angel.
Madara/Kisame/Zetsu
Senior: Madara
Similarity: Apparently working against Pain and Konan
Target: None
A team that has so far done nothing but wait for the other teams to finish their missions. They are apparently working without Pain and Konan for some reason, most likely because Madara doesn't trust them.
Team Hawk
Senior: Sasuke
Similarity: This team has two similarities.
Former association with Orochimaru.
Cursed Seals (Sasuke and Juugo only)
Targets: Eight-Tails (failed)
Due to the loss of five members, the Akatsuki doesn't have the strength they used to have, so Madara enlisted the aid of Team Hawk, whose mission was also the destruction of Konoha. To complete their goals, Madara ordered Hawk to hunt the Eight-Tailed beast while Akatsuki hunts the demon fox. Technically, the members of Hawk are not full members of the Akatsuki, as they do not possess the rings worn by each of the full members.
Zetsu
Status: Active
Similarity: Same Person
Target: Unknown
Not technically a team, but Zetsu has two personalities, effectively making it a team of two and Madara sometimes needs him to go alone. The pair often come into conflict with each other's ideas (one time where one half wanted to see the battle between Naruto along with his teammates against Madara and the other wanting to see the battle between Sasuke and Itachi) though nonetheless obey orders well and are punctual.
Inactive
Orochimaru/Sasori
Senior: Presumably Orochimaru
Similarity: This team has four similarities.
Body modification for eternal youth (Living Corpse Reincarnation for Orochimaru; Human Puppets for Sasori)
Orphaned at young age
Poisonous animal themed names (Snake for Orochimaru; Scorpion for Sasori)
Nicknamed ("Orochimaru the Giant Snake"; "Sasori of the Red Sand"
Target: Unknown
Sasori claimed that he and Orochimaru worked well together during their partnership. However, when Orochimaru defected from Akatsuki after his failed attempt on stealing Itachi's body, Sasori has developed a grudge against his partner.
Itachi/Kisame
Senior: Itachi
Similarity: This team has three similarities.
Elemental users (Fire for Itachi; Water for Kisame)
Animal themed names (Weasel for Itachi; Shark for Kisame)
A last name (unlike the other members) (Uchiha Itachi; Hoshigaki Kisame)
Targets: Nine-Tailed Demon Fox (Failed), Four-Tailed beast (Sealed)
A team that functioned well together and was unbelievably effective. Mission wise; the team completed almost every assignment Pain gave them with little trouble with the Nine-Tailed Fox being the only known exception. Unlike most Akatsuki teams, Kisame and Itachi got along fairly well; Kisame did as Itachi asked unquestioningly and they would often converse casually when not in combat.
Sasori/Deidara
Senior: Sasori
Similarity: Artistic values (Human Puppets for Sasori; Exploding Clay for Deidara)
Target: One-Tailed Shukaku (Sealed)
Formed by the two artists of Akatsuki, Sasori and Deidara worked well for the most part but had conflicting ideas on art. Sasori thought all art was to be permanent, such as his puppets, while Deidara thought art was instantaneous and then gone forever, such as his exploding clay. Sasori, having many connections, was able to get a spy into Sunagakure for years before their arrival, to learn the villages defenses for their raid. The team also had several arguments and debates on plans, Sasori being a impatient man and wanting to finish missions quickly as possible though this is compensated by Deidara's way of executing such plans; the battle against Gaara being an example.
Kakuzu/Hidan
Senior: Kakuzu
Similarity: This team has five similarities.
Invulnerbility (Multiple hearts for Kakuzu; Jashin immortality for Hidan)
Murderously violence associated with ways of severing ties with their villages
Dislike for each other's ideals
Murders to maintain invulnerbility (Stealing hearts for Kakuzu; Maintaining religion power for Hidan)
First kanji of name related with Shogi ("Kakugyo" for Kakuzu; "Hisha" for Hidan)
Targets: Two-Tailed Demon Cat (Sealed), Nine-Tailed Demon Fox (Failed), Unknown Target (Failed)
A very effective yet unruly team; usually doing unrelated jobs and always late. Pain decided to put these two together because of their unique abilities. Hidan, as a result of a "Jashin experiment" could not be killed, even by decapitation, and Kakuzu could easily go into a rage and kill anyone around him, including his partner. Therefore, with Hidan, Kakuzu can go into a rage and not worry about his partners' life afterwards. They have shown the most hostility towards each other due to a conflict of interest; Kakuzu sees the rituals and beliefs of Hidan's religion to be a waste of time, and Hidan sees Kakuzu's willingness to do blasphemous things and his greediness to be unbearable, not to mention that Kakuzu's job as a bounty hunter usually gets on Hidan's nerve. Their team was assigned to capture the Two-Tailed Demon Cat, but later decided to also capture unknown target, because they happened to be close to the Land of Fire after capturing Yugito Nii; after the sealing of the Two and Three Tails, they decided to go after Nine-Tailed Demon Fox.
Deidara/Tobi
Senior: Deidara
Similarity: None
Target: Three-tailed beast (Sealed)
Formed after the death of Sasori, Tobi was introduced as his easily found replacement. Despite Tobi's eagerness to please his "senpai", his childish attitude was seen as a annoyance to Deidara's expectations of the organization. Beyond this, the two worked well together, with Tobi planting much of Deidara's explosive clay underground during their fights. When Deidara was about to blow himself up to kill Sasuke Uchiha, he apologized to Tobi, saying that he too would be caught up in the blast.
Aside from the similarties noted above, certain Akatsuki members have similarties and unique traits among the group.
Immortality/Eternal Youth
Orochimaru: uses Living Corpse Reincarnation to switch into healthier bodies indefinitely.
Itachi Uchiha: claimed to want to obtain his Eternal Mangekyo Sharingan to become immortal (though it turned out he lied to protect Sasuke).
Sasori: changed his own body into a Human Puppet, thus maintaining his youthful looks (though his heart may stop beating of old age).
Madara Uchiha/Tobi: obtained the Eternal Mangekyo Sharingan and achieved immortality, as seen from his advanced age and ability to survive fatal strikes.
Kakuzu: uses Earth Grudge Fear to pluck out the hearts of his opponents and integrate them into his own body to maintain his long lifespan.
Hidan: became the "successful experiment of the Jashin religion's secret jutsu", and can survive even decapitation.
Hatred for the Villages
Orochimaru: rejected for the Hokage position.
Sasori: loss of his parents.
Deidara: village restricts his artistic capabilities.
Madara Uchiha: rejected for the Hokage position, betrayed by his clan.
Kakuzu: unfairly harsh punishment for his failed attempt to kill First Hokage.
Hidan: peaceful ways of his village that clashes with the Jashin ways.
Itachi Uchiha: prejudice and murder of his entire clan.
Unique Abilities/Weapons
Orochimaru: only person capable of using Living Corpse Reincarnation and various self-created techniques, wielding the Kusanagi Sword.
Itachi Uchiha: few surviving users of the Sharingan and Mangekyo Sharingan, only wielder of the Totsuka Sword.
Kisame Hoshigaki: only wielder of the Samehada Sword.
Zetsu: dual personality.
Sasori: only person capable of creating Human Puppets.
Deidara: only person capable of using Exploding Clay.
Madara Uchiha/Tobi: few surviving users of the Sharingan and Mangekyo Sharingan, only wielder of the Eternal Mangekyo Sharingan.
Kakuzu: only user of the Earth Grudge Fear technique.
Hidan: wields a triple bladed scythe and immortality.
Pain: only user of the Rinnegan, six bodies and affinity of all six elemental chakra.
Konan: only user of a paper-style ninjutsu.
Team Hawk
Sasuke Uchiha: few surviving users of the Sharingan and Mangekyo Sharingan.
Suigetsu Hozuki: only wielder of Zabuza Momochi's Giant Sword, unique liquid body.
Karin: only user of Kagura Mind's Eye and Heal Bite.
Jugo: origin of Orochimaru's Cursed Seals.
