Mobians are creatures found in various Sonic the Hedgehog continuities. They consist mainly of anthropomorphic animals. Like humans, they have five fingers (some may have toes). Ungulates have hooves for feet.
Mobians in the Various continuities
The cartoon series Adventures of Sonic the Hedgehog features a world where the general populace is Mobians. However, humans feature regularly in the series in certain communities (e.g. Hill Top Village, Robotropolis).
Sonic Underground also depicts a Mobius inhabited principally by Mobians, although it should be noted that the variety displayed in them is much greater than in previous series. While there are the usual dogs, horses, etc. there are others that bear little resemblance to standard animals, having six arms, three legs, etc. Dr. Robotnik is the only human in the series.
The Archie Comics give an explanation as to the origins of Mobians. In the comics, Mobius is a futuristic Earth. After a human act of aggression towards an extraterrestrial emissary sometime in the year 20XX, the alien Xorda bombarded the planet with powerful gene bombs with the intention of eradicating all humanoid life on the planet. These explosives caused the native animals of the planet to mutate and rapidly evolve, growing larger and more intelligent. However, it should be noted that the evolution of the Mobians may not have been entirely due to the Xorda. The aliens inform Sally that Mobians "contain a sizable percentage of human DNA". It's possible that gene splicing may have been carried out beforehand. After all, Sally calls her race 'Mobo Sapiens.' Another possible result of the Xorda attack could have been the mutation that differentiates Overlanders from ordinary humans, both of which are found on Mobius.
After Sonic & Mega Man: Worlds Collide, the term "Mobian" was eliminated from the comics following the comics' reboot. The term was later reestablished in the summer of 2016, though their planet is no longer known as Mobius. "Mobian" became just a colloquial term to refer to the "antropormorphic animals" that inhabit the Sonic's World.
Post-Sonic Adventure games
Back during the Dreamcast era, SEGA planned to eliminate the Western and European concepts of Sonic. In the games post-Sonic Adventure, Sonic and his friends live on Earth. There is no official name to replace "Mobians" so far.