We’re not talking about the best episodes of the season, necessarily, but what are the segments that you need to see if you are going to go on to the rest of the series and you want to have the full background on what is going on? Here’s my take on it:
• Encounter at Farpoint – The pilot episode which introduces our entire cast and their mission. Most of that is covered in other stories, though. This episode is on the list because it also introduces Q and sets the stage for the way the series will end, seven seasons later.
• Where No One Has Gone Before – Essential because it explains what Wesley is doing for the rest of his time on the show, especially why is always working on the bridge. It also is the first appearance of the Traveler, who shows up a couple of more times
• Hide and Q – The first reappearance of Q, and first mention of the Q Continuum, I think. This episode goes a long way to developing Q’s trickster personality.
• Haven – Introduces Lwaxana Troi and goes deeper into the Troi-Riker relationship
• The Big Goodbye – The first real holodeck episode and holodeck malfuction, also introducing the whole semi-regular concept of “role play” into the series.
• Datalore – A lot of material on Data’s backstory, and the introduction of Lore, as well as references to Data’s creator, Dr. Soongh.
• Heart of Glory – The first Klingon episode, as well as heaps on Worf’s backstory.
• Skin of Evil – The death of Tasha Yar.
With these episodes, you get all the key story points that are important for comprehending the rest of the series. You can add to that, if you want to be a bit more of a completist:
• The Naked Now – Data and Tasha’s liaison, which is referenced in the future
• The Last Outpost – First appearance of the Ferengi
• The Battle – Introduction of Daimon Bok of the Ferengi, who appears again in season seven
• 11001001 – Introduction of Minuet, who appears one more time in a brief but important role
• Neutral Zone -The return of the Romulans, and reference to destroyed outposts which gets mentioned again in the next season.
That leaves 12 out of 25 episodes that you can basically ignore if you want, although you’ll miss a couple of interesting ones if you do. You could also include Coming of Age, as it gives some insights into the background on Wesley and his father, but if you do, you really also have to include Conspiracy. And that seems annoying, since the plot threads for Conspiracy were so conspicuously not followed up on.