Love the TOS cast of characters, and I guess many others do too.
As much as the show and movies have explored Captain Kirk and his merry band, their civilian life post-GENERATIONS still remains a blank slate, mostly. Now we all know novels and fanfics have thrown every kind of theory into an industrial blender especially the infamous Kirk Loves Spock... let’s examine those which seem most fitting if we can. I would like to include the fanfilm Star Trek: Of Gods and Men within this discussion since it seems as close as we’ll ever get to a TOS era epilogue.
James T. KIRK: officially deceased as of GENERATIONS (A.D. 2293). AFAIK, he had no official relationship after Star Trek 4 apart from Antonia who was mentioned in Generations (it ended reportedly in 2284).
Kirk during TOS was always portrayed as an emotionally wounded man that over(?)-compensated with fruitless temporary relationships. It is possible his son David’s tragic death during Star Trek 3 dealt a fatal blow to a possible reconciliation with Carol Marcus and indeed over any sort of long-lasting relationship, reaffirming his duty over family mantra.
SPOCK: He currently exists in the NuTrek universe. I'm unaware of any mention of a wife or progeny during his TNG appearances. It's been previously discussed on this site and elsewhere that Spock wedded Saavik at some point, though I find this theory ridiculous and fanwanky in the extreme.
Spock did experience Pon Farr onscreen one more time after Amok Time, though he was rejuvenated to a younger form during Star Trek 3. Vulcans are capable of indulging in sexual relations at times other than during Pon Farr, but Spock often seemed to go out of his way to suppress his sexual urges. However, his emotional ‘’epiphany’’ during Star Trek: The Motion Picture seemed to indicate a new willingness to embrace more of his human side...including choosing a new mate?
After crossing into the NuTrek universe, it appears Spock willingly isolated himself for 20 to 30 years on an ice planet until he was miraculously discovered by NuKirk. It’s unknown if Pon Farr is a lifelong hormonal cycle or if it is similar to Menopause and Andropause, i.e.: ending at the onset of middle-age, which would have permitted him to survive during his long period of solitude.
Currently Spock lives along with the last survivors of the doomed planet of Vulcan.
Leonard McCOY: As mentioned during TAS ‘’The Survivor’’, Bones was a divorced father during the TOS era. His southern charm made a lady or two swoon in his day, Yeoman Barrows to name one, but the events in FOR THE WORLD IS HOLLOW AND I HAVE TOUCHED THE SKY indicate these two did not last.
McCoy was roughly 137 years old during Encounter at Farpoint, his last onscreen appearance. Given his romantic nature, I would assume for most of the years between 2286 (ST5) and 2364 that the Doc got hitched once again.
Montgomery SCOTT: I really like Scotty, but the guy has been portrayed as the perennial ''loser at love'', falling for the wrong woman (Carolyn Palamas, Mira Romaine).
There was a charming story in DC COMICS' ST series back in the 90s, where Scotty married a childhood sweetheart, Glynnis Campbell, but ending with her death. This wouldn't contradict Scotty's final appearance in TNG's RELICS, where he is flung to the future because of a transporter incident. He shows no concern for a long-lost loved one, and departs for new adventures at the end...
SULU: As revealed in GENERATIONS, our favourite helmsman found the time at some point to become a daddy (and as of ST:P2's WORLD ENOUGH AND TIME, a grampa). That he was ready to go to jail without a thought otherwise during ST 3 makes one wonder if he was with the mother at the time...
CHEKOV: If we give credence to web-based STAR TREK: OF GODS AND MEN (and why not, since it actually has the original actors therein), our young russian lothario ended up with Yeoman Martha from ‘’The Apple’’ episode. Now, the former navigator always seemed to be played as a Kirk on steroids, very much enjoying female companionship.
When reading of Gene Roddenberry’s scuttled plans for third season Chekov, it seemed he might have wanted to live vicariously through young Pavel as he would have indulged in many sexual conquests unencumbered with command responsibility. I'd like to think Gene would have used this to push the envelope of then-current sexual status quo (much like what Kirk and Uhura’s kiss pushed for racial relations), seeing as he himself was being very experimental in those days.
When I saw now-Admiral Chekov and the former Yeoman Martha at ‘’OF GODS AND MEN’’s wedding scene, I at first thought another familiar brunette standing nearby might have been Irena Galliluin from ‘’THE WAY TO EDEN’’ (it wasn’t, darnit, it was actually the belly dancer from WOLF IN THE FOLD). But I thought, how appropriate if it HAD been Irena. I can definitely see Chekov living in a three-way marriage...
UHURA: Again as seen in OGAM, Uhura weds Spock's former rival Stonn. For years it semed as if Uhura never got it on with anybody, but the web-film finally gave her a personal happy ending. Her alternate-reality children she had with Stonn at the beginning of the film seemed a propos for her.