A very good question.
SonicxAmy has never been confirmed on Sonic’s side, but Amy has confessed her love many times in the game, so the ship is canon (one-sided as it may be). TailxCosmo was stated clearly in Sonic X (Japanese version) when (SPOILERS) Tails screams “I love you!” as he shoots her.
The RougexKnuckles and RougexShadow pairings have never been confirmed in game but….oh dear. Well…I could have sworn it used to say on Sonic Retro’s page for Rouge that one of the game creators stated that she has feelings for both of them, but it appears I was mistaken. The only thing that has ever said that is Prima’s Game Guide for Sonic ‘06, but who knows where they got that information? Many might argue that RougexKnuckles is hinted at in certain games (and certainly in Sonic X), but unless there’s a clear “I love you” declaration, then one simply can’t say. So I’m going to have to change my previous assertion in this case, and agree with you, Anon. Neither ShadowxRouge nor KnucklesxRouge has ever been officially confirmed, unless someone can prove to me otherwise.
The Archie pairings I’m not even going to bother listing, since there are so many of them. But if they’ve ever dated in a comic (or, in Amy’s case, declared their love openly for someone), it’s canon.
Vector/Vanilla is Japanese Sonic X canon (on Vector’s side only).