Sonic games have always taken place on Mobius, at least according to the instruction manuals of Genesis/Megadrive Sonic titles released outside of Japan. When Sonic the Hedgehog was released in 1991, Sega of America worked on the back story (the Sonic Bible) -- The story had Sonic living on a planet called "Mobius" (even older concepts in the Sonic Bible had Sonic living on Earth.)
In Japan, of course, this wasn't printed in the manual, leading probably to the only case in history where people on one side of the Pacific believed that a fictional character lived on a different planet than people on the other side did.
Things got even more interesting when Sonic was adopted into various comic book and television series, all of which expanded on the world of Mobius. Finally in 1999 Sega put a stop to this when they released Sonic Adventure and onward, which was a game that was apparently set on Earth (or a Mobius that more closely resembled Earth than previously thought).