In the mid-60's, the television landscape was dominated by comedies, variety shows, and crime dramas. Westerns were gradually fading out. Science fiction was making an inroad, thanks in large part to Irwin Allen's Voyage to the Bottom of the Sea & Lost In Space. Batman, which bowed in January 1966, re-opened a doorway for comics fans that had been closed after The Adventures of Superman had ended 8 years earlier. Spies were taking over, be they serious (The Avengers made their American debut in '66) or not (Get Smart).
Into this mix came perhaps the most famous science fiction series of them all, Star Trek. Creator Gene Roddenberry even went so far as to compare his series with the Western, Wagon Train, which, admittedly, was a bit of a reach. However, the "five year mission" of the USS Enterprise initially lasted three, as a shrinking viewer base convinced NBC suits to end the series in 1969. Of course, you know the rest of the story, how syndicated reruns led to the resurrection of the series as a movie franchise, and Paramount eventually made 4 more series, including one prequel series, to keep the brand active.
But, let's go back to where it all began. Today's generation might think of William Shatner for those goofy Priceline ads, but before Trek, the Canadian-born Shatner was already an accomplished character actor, having made the rounds of shows like The Twilight Zone. His characterization of James T. Kirk, Captain of the Enterprise, came across as being what James Bond would be like if he had to lead a team. It seemed that it was news if Kirk didn't hit on some alien babe in a given episode. In contrast, Mr. Spock (Leonard Nimoy), the rational Vulcan second-in-command, routinely stole the show, being order to Kirk's brand of chaos. Kind of like the older brother having to calm his sibling's frat-boy urges.
When the series was in weekday repeats in the 70's, I must've seen every episode at least 3-4 times each. I do have my favorites, but I couldn't find them on YouTube. We must, then, settle for Roddenberry's take on the counter-culture movement of the period, as Skip Homeier and a young Charles Napier guest star in "The Way to Eden", one of the rare cases where Lt. Chekov (Walter Koenig) gets the girl........
Edit, 8/5/16: The episode was deleted due to copyright issues. Here's a rarely seen teaser for the episode:
It can be said that the mission was allowed to continue when Paramount reached a deal with Filmation to produce an animated version of the series, 4 years after the original show ended, once again on NBC, but only 21 episodes were produced over 2 years, and, thus, it can be suggested that the paperback novels released in the interim period between the original series' end and the release of the 1980 movie, helped complete the mission.