Not too much is known about this game. It was released only in Japanese arcades, with one machine in Europe, so it never made it to the US.
There is info on the story, though it isn't very detailed: Sonic and his two new friends, Mighty the Armadillo and Ray the Squirrel, have been captured by Eggman and are taken to his base on an island. Now they must escape (obviously). Since the game's text is in Japanese, not much detail is available. If anyone can provide more info, please do!
The game was designed to be a "track ball game", where you use a "track ball" to control Sonic, Ray, and Mighty, and use a single button to perform the Spin Attack to get through the levels. There are no enemies, but there are plenty of obstacles in your way that you must destroy with the Spin Attack. It's important to keep moving, because there is always something chasing after you (avalanche, a wall with spikes, etc.), and if you get hit, you lose a chunk off of your life bar. The game also had a 3/4 overhead view and true 3-D graphics with flat-shaded ploygons, like Sonic 3D Blast, but more detailed.
The game DID have one showing in America. JUST ONE! It won critical acclaim at a Consumer Electronic Show(CES) in Vegas, but was never released in US arcades. It would have been a nice Saturn title...anyway, this game's limited release makes it absolutely the rarest Sonic game of all time. The only way Americans can ever play it is by going to Japan or Europe and find an arcade, or finding a ROM of the game, which has not been dumped into one...yet.
Another mysterious thing about the game is the music. The only two zones in the game that are known are "Desert Dodge" and possibly "Metropolis Trance", which were discovered through MIDI files of the zones' themes. There were four other songs that were thought to be associated with the game: "They Call Me Sonic" "King of the Ring" "Sonic & Tails" and "Sonic Electronic". These were actually part of a European-release only CD called "Sonic Arcade". Go figure.
This is all the information I have on this rare game. There was an article on some site about the game from EGM (Electronic Gaming Monthly) magazine. I thought the site got deleted but it just moved to another URL. I'll have to find it...
UPDATE: I have names for the zones as well as a storyline and some screenshots. All courtesy of the Green Hill Zone. Thanks Green. =)