Star Trek is one of those franchises that I've only dipped into occasionally: I never watched much of the shows, and I was more of a Babylon 5, Stargate SG-1 and Battlestar Galactica fan in college.
That said, Star Trek was a huge, enormous influence on every aspect of science fiction, introducing millions of non-readers to what had largely been a closed community of readers. Part of its success here was that it pulled in some of the best writers of the time to help create the show, such as Harlan Ellison and Theodore Sturgeon. Without those influences, Star Trek might not have been the influence that it was.
Go read To Boldly Imagine: Star Trek’s Half Century over on Kirkus Reviews.
- The Fifty-Year Mission: The First 25 Years, edited by Edward Gross & Mark A. Altman. This is the first of two volumes, an oral history of the entire Star Trek franchise. It's a pretty amazing couple of volumes. The editors let every party speak for themselves, and it's like a fantastic documentary for the history of Star Trek.
- Age of Wonders: Exploring the World of Science Fiction, David Hartwell. Hartwell has some good points about how Star Trek fit in with 'traditional' fandom.
- The Cambridge Companion to American Science, edited by Eric Carl Link and Gerry Canavan. I recently picked this book up, and it has some great insights into the relationship between Trek and Fandom.
- The History of Science Fiction, Adam Roberts. Roberts makes a couple of excellent points here: namely that Star Trek was responsible for bringing more women into genre fandom.