Well let's lay it out.
Sonic 1, Sonic 2, Sonic 3 & Knuckles, Sonic Adventure, Sonic Adventure 2, Sonic Heroes, and Shadow the Hedgehog DEFINITELY follow on from eachother in that order (Sonic CD fits in there too, probably between Sonic 1 and 2). This is as far as we can be certain (the Advance games also maybe fit somewhere in here, I dunno, and I'm not considering spinoffs, since I'm just dealing with core games for canonical purposes here)
Sonic 06 is supposed to come after Shadow the Hedgehog (judging by Shadow's personality and his relationships with Rouge, Omega, and Sonic). Largely, it doesn't seem to contradict anything I've listed above (aside from Elise's Emerald...). However, it completely contradicts Rush and Rush Adventure, which themselves do not really contradict anything (Shadow, Rouge, Omega, and the Chaotix don't feature in them, but that doesn't have to signify anything). So we could basically either say that 06 never happened (setting aside the fact that it, um...technically did never happen, you know what I mean), or that Rush/Adventure didn't happen. Given F-man's mention of Elise's impossible emerald, I think the choice is obvious. Personally I actually really like Minus's unusual but imaginative suggestion that it was all just a story Sonic dreamt up.
I'm not considering Rivals because Rivals is just...lol. However, if we were to consider it, it also cannot coexist with 06 OR Rush.
Of course, by this point, we all care far too much.