No.
No they aren't, most likely never will be as if there were any couples made canon disaster would strike.
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No, Shadow doesn't have a romantic relationship with anyone.
Because SEGA officialy accepted relationship between Knuckles and Rouge.
shadow love rouge yes,but knux is love tikal no rouge this is a true!!!!!!!! Rouge is in love with Knuckles. It was revealed in Sonic Adventure 2 Battle. And Shadow loves no one. rouge loves knuckles cause she always flared with him in sonic x
yes shadow dos't know it but i can tell he has a soft spot for rouge and soner or la8er he will tell her the truth As far as we know, Shadow hasn't really taken an intrest in Rouge, but Rouge has seemed to taken intrest in Knuckles. (Well, not really, but we know that Rouge flirts with him a lot to make him irritated)
Rouge has a crush on both. Shadow is bad and tries to steal the Chaos Emeralds, Rouge loves to steal jewels. Knuckles relies on his strength and he can glide, Rouge is the same.