There's essentially no contest the death of Spock in Star Trek 2 has been considered the greatest and most touching moment in the entirety of the Star Trek narrative canon. It has never been equaled before or since and will not be. We've had so many decades to have found out otherwise the case is settled, Spock's death has been seared into pop culture, and rightly so.
Slash fic withstanding, what makes the death of Spock an interesting touchstone in American pop culture mythology is that it is a moment not of eros (per the subsequent decades of slash fic) but of friendship.
I have been - and always shall be - your friend. Live long and prosper.
We live in a pop cultural age where eros so defines narrative it is transposed into and imposed upon depictions of friendship. Yes, even Kirk and Spock, which in some sense robs the death of Spock of its singular power as a pop cultural touchstone, a profession of friendship that is clear.
It was, and is, also a profession of friend by someone who sacrificed his life to save his friend. Although Star Trek's pedigree as a franchise promoting secular humanism is beyond dispute, it's fascinating that the most emotionally potent scene in the entire canon so directly evokes such an utterly religious concern as friendship. After all, Jesus was credited with the words, "Greater love has no one than this, that he will lay his life down for his friends." Spock's decision was a logical one, he was able to restore the warp drive at the cost of his own life so that the rest of the crew might live. But trading Kirk's life to Khan for the sake of everyone else being spared could have also been a "logical" move, even though we know it would not have been the decision Spock would have made.
Choosing the path of self-sacrifice to the point of death to save your friends is certainly human.
I've been considering for years writing about how and why I consider Star Trek to have taken the form of American pop culture mythology in a way that Star Wars cannot, and this would be the moment. Bruce Timm and Paul Dini, if memory serves, once quipped in a commentary on an episode of Batman: the animated series, that you never win the Emmy by going for the Emmy.
George Lucas may have overtly tipped his hand by invoking Campbell's monomyth, but Campbell's monomyth can't be a monomyth. It fails to account for the regional variance in the Faustian legend for one, and for another Campbell's monomyth is not the heroe's journey so much as an American journey. There's nothing about Campbell's monomyth that seems to fit well or explain anything about The Tale of the Princess Kaguya in any of its forms, is there?
Even if I were to set aside my skepticism about the monomyth at those levels, or even about the restrictively male-centered cast of the narrative, the problem of the monomyth is that it is, in a phrase, going for the Emmy. Lucas couldn't keep the narrative about Luke Skywalker. The prequels became about Anakin and lame commentaries on political events without substantially engaging them. And Jar Jar ...
We live in an era in which pop culture narratives become ends unto themselves to a point where we consider the money to be made by the franchises to a point where whatever foundational appeal they may have had becomes secondary. We want our franchises badly enough that there are people who want more Whedon franchises whether or not we have any compelling reason to have more of Buffy or Firefly. We don't want things to reach an irreversible end.
Paradoxically some of the great power of Spock's death would have come from what, at the time, was its ostensibly irreversible nature. We did not yet live in the era of the pop culture retcon, at least not in the way we've seen in the last thirty years. Sherlock Holmes was brought back from death by popular demand but it's been in the last forty years that Marvel comics fans could begin to joke that nobody stays dead, except for maybe Uncle Ben. Spock's death came in an era in which the retcon of the major character death wasn't normative because it wasn't normal to kill off as prominent a character as a Spock.
It had some foreshadowing early on in the Kobayashi-Maru test. Spock calls back to it in his words to Kirk:
I never took the Kobayahsi-Maru test til now. What do you think of my solution?
Wrath of Khan was a story about how Kirk's judgment turned out to be tragically, and even comedically wrong. Way back in "Space Seed" Kirk made a decision that was questioned by both Spock and McCoy. Kirk stood by his decision and decades later, Khan came back for revenge. Popular though it may be for some to say Kirk learned anything at all in Star Trek 2, the power of the story is that Kirk only learned he was willing to cheat death and that he'd never encountered a moment where it was truly unescapable for him. His confrontation with mortality was not even for himself, but through the death of his friend. Spock was willing to pay the price for the failure of his friend Kirk's judgment, however much an accident of circumstance that failure of judgment may ultimately have been. We can't gamble on what failing stars destroy which planets, after all.
That's the thing about failure, it can crash in on you unannounced (or grandly announced by someone like Khan) and there's nothing you could have done to have averted it.
But of course we know Kirk cheated on the Kobayashi-Maru test because he refused to believe in no-win scenarios. What Kirk, perhaps like many an American (perhaps?), didn't count on was that while there may not be many truly no-win scenarios there are many things in life and death where every opportunity has an opportunity cost. In choosing a path we choose to go through things attending that path. Kirk chose to give Khan the chance to form a new civilization after his own ideals, without considering the possibility of what might happen if that civilization failed and Khan blamed Kirk for that failure. Well, in Star Trek 2, we got to find out ...
Spock assessed the situation at the end of the film and saw that there was a way to save as many lives as possible so long as he was willing and able to sacrifice his own life toward that end. The death of Spock became a touchstone in American pop cinema because we'd always been shown that Spock was half human and half Vulcan and his death saving the Enterprise from Khan was a decision and an act that showed the unity of both halves that we knew was always there. Spock was willing to pay the price that he knew Jim couldn't and maybe even wouldn't be willing to pay to save everyone. After all, to borrow a phrase from someone else, even if the spirit were willing, the flesh can be very weak. Kirk went decades without realizing he had a son, after all, and it's not like he managed to be a great lover/husband/father along the way. Wrath of Khan is in some sense a story of middle age and how all the foolish and ill-advised decisions of youth, the decisions you seemed so sure about at the time, all come crashing back into your life in the most embarrassing and disastrous ways possible. What's worse, all of this happened in ways that you couldn't have anticipated and couldn't control. And when they do, who is there to help you walk through it? A friend, a friend who ends up bearing the costs of all the disastrous decisions that you made so that you can keep living.
How many moments in cinematic history get in the zone of Kirk and Spock's friendship, or should we say Spock's friendship to Kirk? Growing up it was difficult to think of another example. As a fan of animation the only possible next runner up to the friendship of Spock and Kirk, for me, would be Woody and Buzz Lightyear from the Toy Story franchise. American popular cinema tends to focus more on the attainment of and sustenance of eros than friendship, which may be why the friendships that capture the imagination capture the imagination so strongly.