An episode with an image as classic as Sulu fencing has got to be considered essential viewing.
"The Naked Time" is one of the episodes from the series to receive a sequel in a later series, in this instance "The Naked Now" from The Next Generation. Its tale of personality traits being amplified sets another franchise precedent ("Singularity" from Enterprise), meanwhile.
This is the first time in the series where the cast can be considered solidified. After the broadcast decisions that left the second pilot aired a little later in the cycle, main characters appear and disappear seemingly at random. In "Naked Time," however, there's Kirk, Spock, McCoy, Sulu, Scotty, Uhura, and even Nurse Chapel and Rand.
Sulu fencing would become an iconic image from the series and a defining trait for the character, even though this is the only time with the character being performed by George Takei that there's any indication of his knowledge of sword fighting. In Star Trek (2009), this element is better integrated into Sulu's skillset.
A couple of recurring elements from later in the franchise also make significant debuts in the episode: Spock (or any Vulcan) struggling with remaining in control of his emotions, and the slingshot concept of time travel, famously featured both in the series ("Tomorrow Is Yesterday") and the films (Star Trek IV: The Voyage Home).
franchise * series * essential * character
Grace Lee Whitney
Memory Alpha summary