From Sonic Retro
In Western continuity, the Chaotix is a group of characters which debuted in the game of the same name. The group exists primarily in the Sonic the Hedgehog series by Archie comics and Sonic the Comic, with a downsized three-member team appearing in Sonic Heroes as Team Chaotix.
The Chaotix is usually comprised of four "main" characters in the game; Espio the Chameleon, Vector the Crocodile, Charmy Bee and Mighty the Armadillo (the latter being dropped in Heroes). Knuckles the Echidna is sometimes viewed as a leader, while Heavy and Bomb who also tag along for the adventure are also sometimes considered.
In video games
The concept of "the Chaotix" being a group was never explored in the video games during the 1990s. In Japan, each cast member of Chaotix visits a mysterious island raised from the seabed by the Master Emerald for different reasons, only to be caught up by Dr. Eggman's schemes in his newly constructed Newtrogic High Zone. The group are forced to work together, but never identify under one banner, and their fate after the adventure is unknown.
In the Western plot of Chaotix, Espio, Vector, Charmy and Mighty are named as Knuckles' friends, who are all on a visit to "Carnival Island" which Knuckles looks after. In both versions, the "Chaotix" name is not used outside of the title screen and level title cards. As a "traveller", Mighty previously had his own adventure in SegaSonic the Hedgehog, while Espio returns as a solo act in Sonic the Fighters.
With the release of Sonic Heroes, Espio, Vector and Charmy are portrayed as being part of a "Chaotix Detective Agency" business, and have usually been grouped under that banner ever since. Here the characters are treated as being reinvented from their previous incarnation, ignoring the events of Chaotix entirely. Vector is the lead detective, Espio is a an expert ninja, and Charmy is a young child.
In other media
Sonic the Hedgehog (Archie comics)
In the Archie comics series, the Chaotix were formed when the primary members ended up working alongside each other to stop Robotnik's threats against the island, and when they were dealing with Archimedes' mysterious actions. Archimedes would eventually become part of the Chaotix when it was revealed that he was just testing Knuckles. Although reluctant to become a team, the members of the Chaotix eventually realised that they best work together to help protect the island. Over time, other members joined the Chaotix, including Julie-su, Ray the Flying Squirrel and Saffron Bee.
Sonic the Comic
In Fleetway's Sonic the Comic, the "Chaotix Crew" are initially introduced with a sixth member, Nack the Weasel, who goes on to betray the group and become a recurring villain. The Chaotix are portrayed as a peacekeeping force in the "Special Zone", coming into contact with both Sonic the Hedgehog and Knuckles during the course of the original print run. Vector is portrayed as the leader, Espio and Mighty as bickering rivals and Charmy (or "Charmee") as the annoying one. The group also make use of the Omni-Viewer, allowing travel between the Special Zone and Mobius.
Sonic the Hedgehog (IDW comics)
Sonic hired the Chaotix to track down the missing Dr. Eggman, who they discover had lost his memory and started going by Mr. Tinker. They later participated in the battle for Angel Island. Then they got briefly infected by the Metal Virus. Sometime later the Chaotix were called in by Jewel the Beetle to investigate crimes committed by the Deadly Six. After that they investigated the strange incidents in Central City caused by Surge the Tenrec and Kitsunami the Fennec. While investigating they encountered Rough and Tumble, who were working for Clutch the Opossum.
Sonic the Hedgehog 2: The Official Movie Pre-Quill
The Chaotix appear working in the Casino Night while Knuckles the Echidna was brought there against his will to fight.