There are fans, there are super-fans…and then there are Star Trek fans.
Their inexplicable rivalry with Star Wars fans notwithstanding, they kind of set the bar for enthusiastic fanbases. In fact, without them Star Trek might have ended up as some forgotten also-ran of a TV show.
The term "trekkie" first arose in 1967, when series creator Gene Roddenberry showed up at a science fiction convention to preview an upcoming episode of the show and was greeted by a mob of enthusiastic fans. And their devotion continued after the show was cancelled in 1969. The first big fan convention was held in 1972 in New York City. Roddenberry attended, and, fed by the show's reruns in syndication, the base of Trek faithful only grew from there.
Like the characters they loved so much, Trek's fans have been innovators. They successfully lobbied NASA to name the very first Space Shuttle the Enterprise. (Source). And when the whole crazy "internet" thing got started, they were among the ones making early use of it. (Source)
Their dedication extended to other things as well: wikis, fan fiction, cosplayers and convention after convention after convention. None of that's unique, of course, but Trek fans—whether you call them Trekkies, Trekkers, or just folks who look good in a set of pointy ears—set the pace that all those other fan bases have followed.
The stars of Trek, for their part, have had a mixed reaction to their devoted followers. After being overwhelmed by fans while attending a parade in his Spock gear, Leonard Nimoy swore he would never appear as Spock in public again. (He recounts the story in his book I Am Spock.) Indeed, the only reason he agreed to take the job in Star Trek II was because they were killing off the character.
William Shatner, for his part, had his own brush with the fan base, notably in an infamous Saturday Night Live sketch in which he admonished a convention full of (fictional) fans to "get a life!" Other members of the cast all have stories of encounters with unhinged fans.
And yet, their stance softened over time as they realized just how much of an impact their work has had. Nimoy obviously thought better about the whole "never play Spock again" thing, returning for numerous appearances and even directing Star Trek III and IV, which restored Spock to life.
In an interview with Playboy magazine, Shatner recounted how he met a Vietnam veteran, a POW who stayed sane in the camps by reciting old Star Trek episodes with a fellow prisoner. In the documentary Trekkies, James Doohan tearfully tells about how he talked a woman out of killing herself. The devotion of Trek's fans knows no bounds, and in the end, the entire cast learned to return their love and enthusiasm.