“Lizard’s Leg and Owlet’s Wing” from the “Route 66” show where Boris Karloff, Peter Lorre and Lon Chaney Jr meet to discuss if their old monster movies can still frighten audiences in 1962. A light hearted episode in a series that featured drama and social realism.
Well, in the real world, 9/11 happened and the producers thought they should do something about it in the President Bartlett Universe.
Another Buffy example would be “Normal Again.” Fans either think the episode was a masterpiece of subversion or want Joss tortured and crucified for the very thought of it. Is reality real, or is is the dream real? And which is reality?
I kinda want both. Maybe not crucified, but he should be at least be given a paper cut drenched in lemon juice for it.
ER episode Time of Death starring Ray Liotta starts off normal until Ray’s alcoholic character is brought in dying of end stage liver failure. We then follow only his story in excruciating minutia. I think Ray Liotta won an Emmy for it.
Minor nitpick:
I liked the episode, but City on the Edge of Forever comes first on chronological basis (based on setting). 
Zev Steinhardt
“It may look like a walnut” from Dick van Dyke, a dream episode with Laura coming out of a closet riding on a sea of walnuts, Danny Thomas as Kolak from the planet Twilo, aliens with eyes in the back of their head and perfect 20-20-20 vision.
Is this the one with the no-thumbs? I remember being very, very frightened of the no-thumbs DVD show. I don’t remember what it was about, only that people were laughing and that made it even scarier. I must have been a toddler at the time but I still remember this, that’s how much it scared me.
To speak to the question of the OP… off-format episodes are remembered and probably receive more praise because… they are off-format. They stick out more.
No one in “City” is meeting an alien for the first time, and aware of it, are they? The only non-human present is neither contemporary to the uncontacted humans, nor meeting humans for the first time himself. Whereas in “Carbon Creek,” the Vulcans are very consciously meeting their first humans–though the humans still aren’t clued in.
MASH had a few but I think the most acclaimed was The Interview.
Big Bang Theory, The Closet Reconfiguration.
During a cocktail party, Sheldon reorganizes Howard and Bernadette’s closet and finds a letter from Howard’s father, which he had to open to figure out where to file it.
Howard, abandoned as a child by his father, never read the letter, which came on his 18th birthday.
Using the loophole in closet organizer-organizee confidentiality (:D) the girls get Sheldon to reveal the letter’s contents.
They then tell the other boys, and Howard is rightfully pissed off. In order to make things right, they all sit down to tell him a different version of what the letter said, only one of which was true (Sheldon didn’t get it and tried to recycle the plot from Goonies).
I found this episode well done and sweet and thoughtful. There wasn’t a lot of the nerd hijinks we normally get, just a man who doesn’t know why his father left and trying to deal with that.
You have the policeman who sees Spock and his ears. Kirk tries to explain it by saying he’s Chinese who got his ears caught in an automated rice picking machine but fortunately nearby there was an American missionary who was also a skilled plastic surgeon…Kirk also tells Joan Collins in the future someone on a distant planet will write the three most important worlds are “let me help”. But neither are aware they are aliens, just strangers with an unspoken past (and clothes thieves).
The previous one they did where the radio station was a space station was better.
That was the ep that really cemented the show as being “about nothing” so it’s probably about as on format as anything.
Community had a lot of good ones like you mentioned. I’ll add the episode where the gang plays D&D with Fat Neil.
ST:TNG maybe “Darmok”. (and Jalad at Tanagra).
Supernatural had one in a similar vein. They had an episode called “Ghostfacers” where the boys run across some people doing a “Ghost Hunters” style of show. The episode is fimled partly in the style of Ghost Hunters.
Supernatural also had an episode where the boys are transported to a parallel Earth where their lives is just a TV show and they are actors. They even joke about how lame their “real” names are.
I think some of the OP’s examples are problematic, at least regarding Star Trek: TNG. The only one of those I would really consider off-format is “Below Decks,” as it introduces completely new protagonists. (I also find it tedious, but that’s just my opinion.) The rest aren’t really big departures from the normal show. “Sub Rosa” is a mild genre experiment, along the lines of “Clues” (mystery story) or “Starship Mine” (Die Hard-esque action movie); it stands out from those others chiefly because it’s done so poorly.
Law & Order’s format was so rigid that when it made off-format episodes, they really stood out. The first was season four’s “Mayhem,” when Briscoe and Logan have to chase down five different murder cases in one episode, with no corresponding courtroom scenes. The biggie was the season six finale “Aftermath,” where the gang witnesses an execution and there’s no investigation or trial. Instead, all hell breaks loose: Briscoe falls off the wagon, Curtis has a fling with a college student (Jennifer Garner, so, can you blame the guy?) and Claire Kincaid is killed by a drunk driver.