STARS (Special Tactics And Rescue Service) was an elite paramilitary anti-terrorist unit headquarted in Raccoon City. It was broken down into two groups: Alpha Team, led by Albert Wesker, and Bravo Team, led by Enrico Marini. In July of 1998, STARS was tasked with investigating the disappearance of several people in the heavily-forested Arklay Mountains. Bravo Team went in first and never returned, leaving it up to Alpha Team to rescue their comrades and get to the bottom of the mystery.
What they found was an isolated mansion owned by Umbrella, Inc., which was populated with various flesh-eating monsters. After a betrayal by Wesker and the destruction of of the mansion, surviving STARS members Chris Redfield, Jill Valentine, Barry Burton, Rebecca Chambers, and Brad Vickers were disbanded by Irons, Brian, who they later learned was really working for Umbrella.
In the novels, STARS (Special Tactics And Rescue Squad) is an elite anti-terrorist group with a branch in Raccoon City. STARS is a national organization and has members besides those on the Alpha and Bravo Teams.
In the comics, STARS (Special Tactics And Rescue Squad) is a single-team group commanded by Ryan Henderson. STARS was the best of the best, but was apparently wiped out by Nemesis when Major Timothy Cain selected them to test the monster's skills during its trial run.
In the original games, there seems to be some debate over just what STARS stands for. Most promotional material for the games state that it is an acronym for Special Tactics And Rescue Squad, but the banner in the STARS office in Resident Evil 2 clearly says Special Tactics And Rescue Service. In light of this, it can be surmised that the banner provides the "official" name.