For anyone unfamiliar, the Hugo (science fiction) awards only have one category(Best Dramatic Presentation) That Star Trek can win in. The other categories are:
Best-
-Novel
-Novella
-Novelette
-Short Story
-Professional Magazine
-Professional Editor(like a magazine editor)
-Professional Artist
-Fanzine
-Fan Writer
-Fan Artist
(There are sometimes others)
They've added more categories since the 60's. For instance, Best Dramatic Presentation used to include any TV episode, motion picture, or short film. They're now divided as "short form" and "long form." They've also added podcasts, graphic novels, et al.
In 1966, there was no winner of Best Dramatic Presentation due to insufficient nominations.
In 1967, 3 of the 5 nominations were Star Trek. One of the others was Fahrenheit 451, and I don't remember the last. The Menagerie won. (As mentioned Above)
In 1968, ALL FIVE nominations were Star Trek. and 2 were awarded. Trouble with Tribbles, and City on the Edge of Forever(As Above). A third Hugo Award went to Gene Roddenberry!
In 1969, there were no Trek contenders, but Neil Armstrong, Buzz Aldrin, and Michael Collins won a Hugo Award for "Best Moon Landing Ever"
Other Hugo noms/wins from Trek are:
-In 1980, Star Trek: The Motion Picture was nominated for BDP.(Lost to Alien)
-In 1983, The Wrath of Khan was nominated.(Lost toBlade Runner)
-1984, Search for Spock. Nom(lost to 2010: Odyssey Two)
-1987, The Voyage Home. Nom(lost to Aliens)
-1992, The Undiscovered Country. Nom(lost to Terminator 2: Judgement Day)
TNG
-1988, Encounter at Farpoint. Nom(lost to The Princess Pride)
-1993, The Inner Light. Won
-1995, All Good Things. Won
-1995, Star Trek: Generations. Nom(lost to TNG-All Good Things, lol)
-1996, Star Trek: First Contact. Nom(lost to Babylon Five-Severed Dreams)
-1998, Star Trek: Insurrection. Nom(lost to The Truman Show)
DS9
-1996, The Inner Light. Nom(lost to Babylon Five-The Coming of Shadows)
-Trials & Tribble-ations. Nom(lost to Babylon Five-Severed Dreams)
ENT
2003-Carbon Creek. Nom
2003-A Night in Sickbay. Nom(both lost to Buffy-Conversations with Dead People. 2003 was also the first year that film and tv were divided into separate categories)
I believe the first Kelvin film was nominated also. I'm not sure why I wrote all this. Enjoy, I guess.