Ye gods. This franchise is as big as TenchiMuyo. It's an abomination. It really is.
I am not even going to try and list all the platforms the games appeared on. Let's just say that the GameGear? and the MasterSystem? got most of the early games under different names, and that the GameCube gets the later ones (under a 'DirectorsCut?' label) I'm pretty sure there were some for the short lived NeoGeo? HandHeld? and I know that the ThreeDee? one, at least, started in an ArcadeMachine?.
SonicTheHedgehog/TheAdventuresOf?. Incredibly cartoony, no continuing theme. Each episode EggMan? build a robot or hatches a silly plan, his minions mess it up and then Sonic and Tails make him look silly.
There were several series of that. The later ones included a moral at the end. Sometimes this was sensible. Sometimes it was "Remember kids, don't get run over by a SteamRoller?"
SonicTheHedgehog/SonicSM (Sonic Saturday mornings) - they never gave this series a name seperate from 'the adventures of' which it interleaved with. DarkFuture? FreedomFighters?. Coninuing plot. Damn good - and I finally found all of it. PoingPoingPoing.
SonicTheHedgehog/RockAndRoll?. Um - a rather differently drawn sonic and his brother and sister invented a whole new canon as they travelled a different world trying to put the princess on her throne, whilst EggMan? threw more robots at them, which they defeated with flashbacks to 70s episodes of JosieAndThePussyCats?. (Well, sorta. They played music.)