Oddly enough.. Sega's Sonic (I'm not considering Archie's Sonic) and Shadow have never ever expressed any romantic feelings toward anyone.
Sonic actively avoids Amy, and in that game we don't talk about, he never seemed to like Elise more than just as a friend.
Shadow also hasn't expressed any feelings toward anyone but Maria because he's too edgy for romance... or friendship.
Neither have even mentioned wanting to be in a relationship... which is weird, especially considering Sonic's cool-dude personality and inflated ego.
Edit: Same goes for Eggman. Too busy failing at taking over the world to get busy, I guess.
Edit 2: but this shouldn't really count as proof labeling any of them to be asexual. It could just be plot coincidence or writers not caring to cover those sides of them.