Robert Bloch loosely adapted his story "Broomstick Ride" as "Catspaw." Jerome Bixby has stated he started "Mirror, Mirror" with his own story "One Way Street" in mind.
I'm not sure adaptation is the correct word there, though. Bloch borrowed certain details from "Broomstick Ride," like the name Pyris for the planet and the use of a pendant effigy for a spaceship, but the actual plot was different. And the only thing "One Way Street" has in common with "Mirror, Mirror" is the basic idea of a protagonist finding himself in a parallel timeline. So those are instances of drawing on inspirations rather than direct adaptations.
How "official" an adaptation does it have to be to count? Like that ENT episode that played out very Enemy Mine?
Telling a broadly similar story is not an adaptation, more just an homage or pastiche. An adaptation is taking a specific work, with permission and with credit given, and reinterpreting it into a different form. If the credits explicitly say that it was based on a pre-existing work, then it's an adaptation. Otherwise it's just drawing on an influence, something that all fiction does to one degree or another.
Or that TNG that ended up having to credit Laurel K. Hamilton due to...ahem, similarities? (Although her book wasn't sci-fi, but still.)
There is no TNG episode that credits Laurell K. Hamilton for anything; indeed, Hamilton didn't start to become a prominent writer until around the time TNG ended. Hamilton's only connection to TNG is writing the tie-in novel
Nightshade before she became famous. That was actually her first novel, unless you count a fix-up of several short stories which came out in the same year.
I have heard that "Sub Rosa" is often compared to Anne Rice's
The Witching Hour, but no credit was ever given to Rice (and both works are influenced by
The Ghost and Mrs. Muir, so I gather).
Similarly, The Motion Picture was apparently inspired by TOS: The Changeling, although John Meredyth Lucas received no screen credit and the screenplay was actually a direct adaptation of Phase II: In Thy Image. To be honest, I'm unclear on the development lineage there, and why Lucas got no credit.
Similarity does not prove adaptation. Different people end up accidentally telling the same story all the time; indeed, the most common reason why freelance episode pitches get rejected in TV is "We're already doing that one."
Personally I find that TMP bears a striking resemblance to the animated episode "One of Our Planets is Missing." A cosmic cloud entity of proven destructive potential is heading for an inhabited planet, the
Enterprise enters the cloud to try to stop it, it deals with the cloud's defenses, it determines the entity is intelligent and makes its way to the brain center, Kirk orders Scotty to ready the ship for self-destruct if necessary, Spock mind-melds with the entity to communicate, and the understanding he gains leads to the solution, with the entity heading off to other realms. And given that Alan Dean Foster, who adapted TAS for prose, also wrote "In Thy Image," the original story outline that TMP was based on, for decades I assumed that he'd been influenced by "One of Our Planets." But when I finally read "In Thy Image," I discovered that it bore far less resemblance to the TAS episode -- that most of the similarities had been added when Harold Livingston, a writer with no TAS connections, had turned it into a screenplay. So what I thought was direct influence was apparently just coincidence.
If TMP had been intentionally based on "The Changeling," credit would have been given. If not, Lucas could've sued. He lived for 23 years after TMP came out, so he would've had plenty of time to sue for, and earn, credit. The fact that he didn't suggests that either the similarities were coincidental, or the influence was indirect enough that it didn't qualify as an adaptation. ("In Thy Image" was itself inspired by "Robots Return," an unused story idea from Roddenberry's failed
Genesis II series premise. It's possible that Roddenberry drew on "The Changeling," consciously or otherwise, in conceiving of "Robots Return," but Foster and Livingston may have had no knowledge of that. In any case, it's an indirect enough line of influence that it doesn't qualify as an adaptation.)
If one wants to broaden the criteria, there are episodes that are clearly beat-for-beat adaptations of other stories, that are not science fiction, at least in cases when no credit was assigned. The foremost example here is probably TOS: Balance of Terror, obviously (and allegedly admittedly) adapted from The Enemy Below.
Again, it's an abuse of the word "adaptation" to use it in that context. That is an homage or a pastiche. It's telling a distinct story inspired by an earlier work. It's only an adaptation if you actually pay for the rights to retell the same story.
Every work of fiction is influenced by earlier fiction or real-life events. If you broaden the definition of "adaptation" to any and all influences, then everything would be an adaptation, and that renders the label useless.