I know it's a vastly unpopular answer, but while The Wrath of Khan is, of course, considered to be the "best" of the original-crew films, I have personally always found the very first film, Star Trek: The Motion Picture, to be the one that draws me back for repeated viewings.
Like the J.J. Abrams re-boot (which I thought was awesome... saw it several times in the theater), ST:TMP really sought to "re-boot" and perhaps even "re-imagine," in its own way, a franchise long-thought by 1979 to be relegated to the comic-book and paperback-adaptation/expansion fringes of sci-fi media.
From a production standpoint, it was a huge undertaking of design conceptualization---an opportunity to show "modern" incarnations of the technology and ideas that the original late-1960s series certainly attempted but found itself restricted in its execution by time and budget concerns.
And from a story standpoint, it's very adult in its depiction of the main characters several years after their successfully completed "five-year mission"---particularly Kirk and Spock, both of whom are on personal journeys amidst their quest to save Earth from "a thing out there" that, of course, can only be stopped by the newly-refitted but very-much untested Enterprise, "the only starship in interception range."
Kirk is contending with the first pangs of age onset after having been transferred from starship command to a desk job at Starfleet Headquarters, using the V'Ger emergency as an excuse to get back into the action of command---going so far as to pretty much steal "the center seat" from his own recommended replacement, Will Decker. Talk about ego and insecurity, LOL.
Spock, on the other hand, is drawn to the mission at the apex of his Kolinahr ritual of emotion purging on Vulcan, responding to his own extra-sensory perception of V'Ger's entrance into local space. He is strangely compelled to seek out what he perceives to be a profoundly organized and efficient intelligence source. Late in the film he discovers through mind-meld with part of the marauding space probe's enormous starship that V'Ger is, in fact, a living machine searching for its creator... and searching for answers to the same questions that he has been pondering in his own Vulcan way, right up to the very last seconds, it would seem, of the ancient Vulcan ritual designed to "purge all remaining human emotion"... the query set that serves as a lynchpin for the film's emotional landscape: "Is this all that I am? Is there nothing more?"
It could be argued that Kirk himself, at his desk on Earth, despite being promoted to admiral and head of Fleet Operations for Starfleet Command after his original five-year mission, was asking himself the same questions---albeit from a more ego-based perspective related to his own fears regarding aging, usefulness, vitality, perhaps even virility. Is this all that I am? Is this the end of my career? I should be out there, commanding a crew...
Admittedly, the film impacted me much differently as a kid and I was more interested in the film's lush Jerry Goldsmith score and the copious cool shots of the bitchin' Enterprise filming model so I could mimic the on-screen shots with my own toy/model like many kids did with their X-Wing Fighters or whatever they were into... LOL...
... but as an adult, the film has taken on a much more adult tenor in my reception. It's a film about spiritual journeys, about personal evolution, about the search for truth and answers---whether you're a human, a Vulcan or a mechanical space probe.
It's also, largely, about obsession and misguided energies that, despite self-perceived legitimacy at their start, result in cascading consequences---often negative in nature.
V'Ger's journey results in the disintegration and digital storage of entire galaxies---starting, in the film's timeline, with the digitization of three Klingon cruisers, but revealed later to have included all objects on its multi-century journey across the cosmos. The civilizations it encountered were effectively wiped off the cosmic map, relegated to patterning for data storage.
Kirk's ego-based quest pushes a young officer's dreams of starship command out of the picture---and his own lack of knowledge regarding the refitted Enterprise threatens the safety of the crew, and the success of the epic mission, more than once during the film's progress.
And Spock, under orders from Kirk to reveal any telepathy or insights regarding the alien intruder, juggles his own duties as a recommissioned Starfleet officer with his own inner struggle for peace between his human and Vulcan halves---his emotionality and his intellect. While he is still seen as a trusted and vital advisor to the legendary, albeit logistically handicapped, starship captain, Dr. McCoy questions when push comes to shove whether Spock will ultimately "put his own interests ahead of the ship's."
It's a story that really takes the beloved Kirk-Spock-McCoy triumvirate from the original series and challenges the audience's notions of just who these men were... and who they are now, recontextualizing their humanity (even Spock's) not only in the face of great peril from the outside, but as agents of check and balance for/against each other as their internal worlds undergo some serious rite-of-passage transformations.
When Paramount released the Director's Edition a few years back wherein Robert Wise and a digital special-effects team were given access to finish segments that were "rough," at best, and do an all-important second-swipe edit of the film (that they weren't able to do for the original due to an insane production schedule which resulted in no test screenings, no remixing, no "final cut," as it were), the streamlined, remixed, "complete" vision of the picture really helped editorially highlight the aforementioned themes a bit more by removing many, if not all, of the distractions with regard to draggy pacing, cold sound, inconsistent special-effect renderings, etc., to let the elements swim together MUCH more effectively.
Considering the monumental task of preparing this epic film and bringing such a complex character story to a science-fiction film in the wake of Star Wars' gigantic cultural impact only a couple years beforehand, I return to this picture again every few years and revel in what a miracle of teamwork and production genius it really was.
Admittedly, it has its flaws, even in the Director's Edition, but ST: TMP was an ambitious piece of work that attempted to bring a 2001: A Space Odyssey sensibility to the Star Trek universe at a time when the "obvious" route, commercially speaking, may have been a film more along the lines of The Wrath of Khan so as to ride sci-fi action/drama wave of Star Wars and, to a lesser degree, its TV-clone, Battlestar Galactica.