Sonic and Rouge the Bat do not seem to have any dislike for each other, despite the latter having antagonized Sonic's friends, notably Knuckles, on various occasions. In fact, they appear to be on good terms. They were initially enemies when they first met (though they did not interact until much later), mainly because Rouge was working with Shadow and Dr. Eggman, but they became allies towards the end in order to save earth. Also, after Shadow's supposed death after defeating the Finalhazard, Sonic comforted Rouge by giving her Shadow's Limiter Ring, showing that he had come to care about Rouge's feelings.
Most of the time, the conversations between Sonic and Rouge are often "probing", camouflaged by jokes, but Sonic loves to joke and talk lightly, while Rouge is a sarcastic person. Still, both Sonic and Rouge enjoy these conversations that play out their "good-natured" rivalry, and can think of each other as people they can rely on in times of need, with appropriate levels of trust and caution. Rouge's presence in Sonic's life brings many new developments to the adventures he goes through.Overall, Sonic has a professional relationship with her. While they can work well together in combat, Sonic does not usually expect Rouge to contribute to efforts that means saving the world of the goodness of her heart. Regardless, he appreciates her help, even if she does so for her own benefit.