Show dates:
Start: 1966 September 8
Ended: 1969 June 3

Current IMDB Rating: 8.6 (based on 9,876 votes, and no I didn't make that number up)

Wikipedia wrote:

The show tells the tale of the crew of the starship Enterprise and its five-year mission "to boldly go where no man has gone before." The original 1966–69 television series featured William Shatner as Captain James T. Kirk, Leonard Nimoy as Spock, DeForest Kelley as Dr. Leonard "Bones" McCoy, James Doohan as Montgomery "Scotty" Scott, Nichelle Nichols as Uhura, George Takei as Hikaru Sulu, and Walter Koenig as Pavel Chekov. During its original run, it was nominated several times for the Hugo Award for Best Dramatic Presentation and won twice: for the two-parter "The Menagerie" and the Harlan Ellison-written episode "The City on the Edge of Forever". After three seasons the show was canceled and the last original episode aired on June 3, 1969. It was, however, highly popular with science-fiction fans and engineering students, in spite of generally low Nielsen ratings although later demographic profiling techniques indicated the series was appealing to a highly lucrative audience. The series subsequently became popular in reruns and a cult following developed, complete with fan conventions. Originally presented under the title Star Trek, it has in recent years become known as Star Trek: The Original Series or as "Classic Star Trek"—retronyms that distinguish it from its sequels and the franchise as a whole.

This is the best trailer I could find for this series. It is a trailer for its remastered DVD's, which came out only a few years ago.