The 1 thing I always think of in a new Sonic game is 2 player co-op. Sonic 2&3 had it, Sonic Advance 3 had it, and Knuckles Chaotix had it. Soic 2 is one of the perfect games for me because of the co-op that me and my sister used. I have dozens of games that have a online, system link, or split screen co-op to them.
Look a Super Mario Bros. Wii, that game could have been a 2-4 player Sonic game if SEGA used my idea that I had for a few years now. It doesn't need to be 4 player, but something like LEGO Star Wars where 1 player can switch between Sonic and Tails with a dropin out co-op for a friend.
Go back to the roots of Sonic 2&3 by just having Sonic and Tails in it. With the 2 characters the game can have puzzles like the 2 to hit 2 buttons to open a door, use Tails to lift Sonic to areas he couldn't reach alone, and beat Badniks with shields by having Sonic stand in front as Tails attacks from behind.
This game could be on any system. Xbox 360, PS3, and Wii could use their online multiplayer, while phone and other handhelds could just have offline multiplayer. New characters could be DLC (did I just say that?). Sonic 4 is on all of those platforms and Sonic 2 is on even more.
This new game can be a download only game too. Sonic may have too many friends these days, but having one in a game with him is better than none (looking at Sonic 4). Sonic is my favorite thing and I want to enjoy it with a friend.