Even though both Sonic and Rouge are good friends with each other's rivals, the two haven't been shown to dislike each other. They have had some conflicting encounters, but appear to be on good terms.
Sonic and Rouge first meet in Sonic Adventure 2, where Rouge is Knuckles' rival. Sonic and Rouge do not interact until the last story, where the ARK is about to hit Earth. They, along with Eggman, Tails and Knuckles, team up to stop the disaster. After the fall has been stopped, Sonic and Rouge talk, and Sonic gives Rouge Shadow's gold ring.
In Sonic Chronicles: The Dark Brotherhood, Rouge flirts with Sonic and calls him by the nickname "Big Blue", which she uses again in Sonic Generations.
In Sonic Generations, Rouge is one of the guests at Sonic's birthday party and Sonic treats her like his other friends. One side mission in Seaside Hill involves Rouge helping Sonic by making Egg Pawns fall in love with her. The level has a romantic design in this mission.
Although they are on good terms, they have had occasional fights. In Sonic Heroes, Team Sonic and Team Dark get into a fight, although the teams later team up to defeat Metal Sonic. In Sonic Battle, Rouge challenges Sonic to a fight and demands him to work for her and get gems if she wins. Sonic manages to win the fight. The two also compete in Sonic Rivals 2 and in Sonic Free Riders, their teams are rivals.
Sonouge is not as popular as other ships such as Sonamy and Sonally for Sonic and Knuxouge and Shadouge for Rouge. The ship is sometimes shipped alongside Shadamy. Other times, it is shipped alongside Silvamy and Shadaze, where each pairing represents common traits. Sonic and Rouge represent freedom.