It's established that the Borg saw Humans as a unique and interesting opponent with very little to offer technologically. The Borg wanted to assimilate Humanity's wisdom, or at least remove them as a future threat.
Am torn on this one, but would have to go with 'Best of Both Worlds' personally.
It was fantastic sci-fi in general.
The Borg were actually threatening, and all but unstoppable, back then. Having seen what the Borg could do in 'Q-who' then seeing that cube again on the viewscreen in Best of Both Worlds, followed by Picard's "Contact Starfleet.... tell them that we have engaged the Borg" STILL sends shivers down my spine.
The music/score was unique, epic and far superior to the mostly generic stuff we got in later seasons/episodes.
Brilliant cliffhanger at the end of the first part - I recall being practically sat on the edge of my seat, Riker saying "Fire" and then... 'To be continued' - Arrrgh! The wait between episodes felt SO long!
The Borg treating the 39 ship sent to combat them as a mere inconvenience - this was a first for Trek. Actually seems that the impact that this had, whilst significant at the time, almost increased over time ,with many describing it as "the Federation's 9/11".
The ridiculous Borg Queen wasn't around to ruin them as she did from 'First Contact' onward.
TOS: Never really got into it. The one with the nuclear weapons platform that nearly set off WWIII was kind of neat.
TAS: Never saw it.
TNG: "Inner Light" and "Family"
DS9: "In the Pale Moonlight" and the one where O'Brien spends 20 years in prison in a few hours
VOY: "Year of Hell"
For one thing, it just doesn't make any sense for the Borg, whose stated purpose is to assimilate cultures for their technology, to go back in time and assimilate earth before they developed any interesting tech. This is a really fundamental flaw in FC which unfortunately, brings it down.
I believe it was stated somewhere in Voyager that they don't just assimilate cultures with useful tech/biology, they also assimilate cultures who pose a threat. The Queen said in "Dark Frontier" that humans were unremarkable, but they were dangerous. Hence their backup plan to go back in time and eliminate the threat before it started.
"It's not safe out here. It's wondrous, with treasures to satiate desires both subtle and gross. But it's not for the timid."
Overall, I would have to say Gravity. I love the friendship/tolerance between Tuvok and Paris, and this episode really explored that, as well as giving an interesting view into Tuvok's past, and by extension, the Vulcan psyche, as it was the first time an established character was acknowledged as having 'needed therapy' as a child, and how that mental illness (for a Vulcan, young Tuvok would have been considered to be mentally ill, where a Human child would simply be considered to be being 'emo') was handled and how that then shaped the character.
I have to separate the films...
Wrath of Khan: So many things which I love about this movie. The only thing which never sat easy with me, was the reactions to Khan himself. Yes, in the movie, he is fantastic. In Space Seed, he was fantastic. But. Kirk faced 'bigger foes' in his time, so for Khan to suddenly come back as Kirk's Ultimate Nemesis... Sorry, but I never bought into it, and no matter how many times I watch it, it never seems plausible. Other than that, I think as films go, it has everything. I wish they'd kept in the scene which revealed that Preston was Scotty's nephew. When I first saw it, I thought "What the hell is he playing at? Carrying a dead guy onto the bridge? WTF?! That's what sickbay's for!" When I realized that he was carrying his nephew, in the hopes that McCoy would be able to save him, the scene gained a LOT more emotional weight... Every time I see Spock's death scene, it chokes me up. There're bits in Search for Spock which have similar weight (and as for the Vulcan priestesses leading Spock's gurney on Mount Selaya... ) but overall, it doesn't quite meet the standard set by its predecessor...
There were things I liked about all the films (even Insurrection, which was pretty cringeworthy) but my favorite of them is First Contact.