After the Battle of Yavin, Luke felt that he wasn't getting enough special treatment. He wanted to stay in the Alliance, but wasn't too keen on being told what to do by people who did not blow up the Death Star. He petitioned General Dodonna to create a new flight group that would more or less go around the Galaxy doing whatever they wanted. Dodonna thought this was a terrible idea, but was busy with real work, so he referred Luke to Mon Mothma. Mon Mothma saw the value of elevating Luke to a high public profile, and also saw the opportunity to come into close contact with much younger men, so she agreed. Luke named the squadron Rogue Squadron because he thought that Rogue was a shade of red. He contacted Sullustan talent scout Tenb Mumn and told him to go recruit the best pilots he could find. Luke also forced Wedge to join by threatening to point out that he had only survived the battle by leaving before it was over.
After a montage of pilots arriving, set to the Top Gun Anthem, Luke and his squadron were ready to kick some ass. Largely the squadron was used to support rescue missions and other "top secret" type stuff. Luke had no intention of entering them into any kind of direct combat. Luke eventually got bored with this stuff, so he took the entire squadron to Hoth, where he would continue to try and nail his sister. The rest of the pilots tried to avoid that akwardness, and just spent their time in the hangar adapting their crappy snowspeeders to the cold. When the time for battle came, they were ready, and attempted to take down the Empire's approaching AT-AT's. They were successful with two, but lost several pilots and speeders. Their actions distracted the Imperials long enough that most of the Rebel commanders were able to escape.
After the Battle of Hoth, it was clear that Luke was not particularly interested in being a team player. Wedge became the commander of the squadron and leveraged his brief marriage to Mon Mothma to secure even more autonomy for the group. Wedge streamlined the group and took more important missions. He was very selective about membership, promoting an environment of elitism. As the Alliance began preparing for the Battle of Endor, Wedge broke up the group in order to spread their strength among the three satrfighter types. Those that survived reformed Rogue Squadron after the battle and continued on under the banner of the New Republic. After Endor, Rogue Squadron opened up their membership a little and started bringing in a sorts of crazy new members.
Later Members of Note
There were a ton of other people who claimed to be members of Rogue Squadron, but most of them were liars.