In a similar situation to Marvel vs. Capcom 3, someone from Sumo Digital has reached out to the official Sonic forums asking for suggestions for DLC characters, with the stipulation that at least 1,000 people have to have voted for the same character by December 1st, and the top three will be possibly added as DLC characters pending approval from higher-ups at Sega and Sumo. There's no guarantee that the winners will actually become DLC, but there's no harm in voting. DLC characters already on the disc (Shogun and Football Manager) aren't included in the poll for obvious reasons. The original post and links to the petitions for each character can be found here, but I'll also link the individual petitions in this post.
At the time of this writing Hatsune Miku is the closest to meeting the goal at 958 votes (fucking Sega fans), with Segata Sanshiro in second at 650 votes. Please vote so we can get awesome characters like Segata Sanshiro, Kazuma Kiryu and Sketch Turner instead of fucking terrible ones like Hatsune Miku, Hatsune Miku and Hatsune Miku.
Edited on 11/25 to add two new options, Ecco the Dolphin and Spiral Knight.