Otherwise known as That 3D Fighting Game Sega Made That For Some Reason Starred Sonic The Hedgehog.
The story of the game goes like this: in 1995, Sega released an awesome (and sadly forgotten) fighting game called Fighting Vipers. One of the game's character designers, Masahiro Sugiyama, thought it'd be funny to secretly slide both Sonic and Tails into the game. While they were never playable by the public in arcades (though the assets are in the game and are playable via hacks), Sonic boss Yuji Naka thought the idea was so great that the pair deserved their own fighting game.
And so in 1996 Sonic the Fighters - amazingly, Sonic's first true 3D appearance - was born.
A 3D arcade fighting game built roughly on the bones (and controls) of Virtua Fighter's technology, which included nine playable characters, three bosses and a further five unused fighters that, again, are accessible only via hacking.
Because this was a Sonic game, it was also a relatively simple experience, lacking in the elaborate moves or combos that more serious fighting games are renowned for. After all, it had to be playable, and enjoyable, for young Sonic fans.
Sadly, the original arcade version saw only a limited release outside of Japan, so the only way most people in the West have experience with the title is thanks to its re-release as part of 2005's Sonic Gems Collection, a compendium of older and often rarer Sonic games released on the PS2 and GameCube.
Like many 3D games from the 1990s, Sonic the Fighters hasn't exactly aged well (though it's clean cartoon style has it looking better than, say, Virtua Fighters), and many fighting game fans dismiss it for its simplicity. They're missing the point, though. The point here was that you could take control of Sonic and, rather than living in fear of spikes and little robot animals, go to town on people. Including Tails. How many other games let you punch Tails in the face, over and over, until he goes down?
Exactly. Some, but not nearly enough.
NOTE: To stop you asking, Sonic Battles is worth its own piece. This is just about Sonic The Fighters, OK?