Mobius (or Planet Mobius) is a place name shared by several different settings in various English-language Sonic the Hedgehog products established in the 1990s. Locations called Mobius are featured as primary settings for the events of comics (Archie's Sonic the Hedgehog and Fleetway's Sonic the Comic), books (the UK's series of gamebooks and four Virgin Publishing "Martin Adams" novels), video games (Sonic Spinball and Dr. Robotnik's Mean Bean Machine) and American cartoons (Adventures of Sonic the Hedgehog, Sonic the Hedgehog, commonly known as "SatAM", and Sonic Underground). Although all these different media share "Mobius" as a name for the planets on which they are set, these worlds are depicted in varying ways.
The name "Mobius" was not used by the authors of the games' Japanese manuals; the earliest use of the word as a place name in Sonic the Hedgehog's backstory can be found in the Sega of America "Sonic Bible" documents.
The US-produced Sonic games Sonic the Hedgehog Spinball (16-bit) and Dr. Robotnik's Mean Bean Machine were developed to tie into the continuities of the US "SatAM" and Adventures of Sonic the Hedgehog cartoons and, as such, their English-language manuals explicitly state that they take place on Mobius.
Depictions of the planet vary depending on the media it is portrayed in. In the Archie comics, Mobius is a future version of Earth, after various catastrophies have destroyed (most of) human civilization. The planet is now populated by Mobians (animalistic beings mutated from "normal" animals) and is ruled by a dictator, Dr. Robotnik, who orginally went by the name of Julian Kintobor before he became a dictator trying to destroy all Mobian life, and trying to turn them into Robots (considered as "Robians") via roboticization. Earlier in the comic series it was mentioned that Mobius existed in an entirely different universe than that of Earth that can be reached through the Cosmic Interstate, an intergalactic road that connects different universes and realities across time and space. It's possible that Mobius is meant to be a future version of an alternate Earth. This version of Mobius is also populated by Overlanders, four fingered humans who survived a genetic bomb attack.
The SatAM version is similar to the Archie Comic depiction, but it being a future Earth is never mentioned during the series run.
In Sonic Underground, the same kind of setup is used, but no reference to Earth is made (nor is Robotnik's first name particularly mentioned). Overlanders are present and a bit more plentiful as only those that break Robotnik's laws become Roboticised.
In Adventures of Sonic the Hedgehog Mobius does not have a dictatorship and Dr. Ivo Robotnik is shown trying time and time again to take it over (and usually failing miserably). Overlanders are not portrayed but instead five fingered Humans are shown.
Sonic the Comic portrays Mobius in a style similar to the early games, as the planet was divided into "Zones", each with a distinctive landscape and climate. At the start of the comic Robotnik was not the ruler but eventually took it over. He subsequently was overthrown, although he tried repeatedly to regain his position as dictator. Mobius and Earth are separate worlds in this comic. This same aspect was reflected in the Archie comics.
In the newest Sonic cartoon, Sonic X, Sonic, Robotnik, and many others are transported from an unnamed planet into present day Earth. It is speculated that the unnamed planet could be Mobius. However, there is no substantial evidence to back up or deny this claim, and since there has been virtually no mention of Mobius in the country Sonic X was made (Japan), many people do not believe it is intended to be that way.
In the Archie comic continuity, Downunda is a continent on Mobius, located in the southern part of the planet. Consisting of mostly desert plains, the continent is inhabited by, and protected by, the Downunda Freedom Fighters. It was originally the location of Echidnapolis and the Master Emerald until it was sent to the sky to avoid a meteor strike, leaving behind a massive crater.
For a period of time, Downunda was ruled by Crocbot and his dingo robots, with help from Dr. Robotnik. Efforts by the Downunda Freedom Fighters, along with assistance by the Knothole Freedom Fighters, helped to stop his rule.
In the Fleetway Sonic the Comic, the most prominent locations on Mobius included the Emerald Hill Zone (Sonic's usual base of operations), the Metropolis Zone (the planet's largest city, from which Dr. Robotnik ruled the planet during his time as dictator), the Floating Island (home of Knuckles the Echidna), and the Never Lake (location of the chain connecting Mobius to the Miracle Planet.