I'd given some thought over this a couple of weeks ago.
My idea for a Sonic game would be something Sonic Adventure-ish. I suppose I'd like to see a plot where Sonic and Tails come across the Knothole Freedom Fighters for the first time (Sally Acorn, Antoine, Bunnie, Rotor, and possibly NICOLE), all sporting their latest redesigns from the comics. It'd basically be about Sonic and Tails teaming up with the FF to battle Doctor Eggman. The following characters would have their own gameplay styles, which is where I drew the similarities to Sonic Adventure. Sonic - Speed/Platforming Tails - Flight/Platforming Sally - Speed/Platforming/Stealth Antoine and Bunnie - Beat-em up Werehog-style missions Rotor - Mech-shooting/Some platforming
The game itself wouldn't be like Adventure where it wouldn't have you picking a character and playing as that character only before being able to unlock the next one. Rather, you could freely choose when to play as a certain character, in a way where doing a character's missions in a certain order wouldn't affect the storyline.
As for a name of this fan-game, I haven't really taken the time to think of a very good one.
EDIT: Aaaand I just noticed MetalSkulk's post right above which completely changed the topic. I'm good at this, aren't I? :P