How many times did Doctor McCoy actually say that?
That exact phrasing? Memory Alpha has catalogued 5 in the prime universe, and 3 in the movieverse. Plus 5 more that I’d say match the pattern meaningfully (reversing the order, altering the punctuation, or using a synonym for doctor), and another handful where he protested he was a doctor without specifying what he was not, or vice versa. (All in the prime universe…the movieverse has hit the exact phrasing every time they’ve gone to the well.)
Have you read that new book called “Damn it, Jim!”? It’s by Ima Doktor and Nada Brickleyer. 
Flees room, holding nose.
My favorite instance was in Voyager, where the Emergency Medical Hologram is complaining about people not turning him off when they’re done. He ad-libbed the line “I’m a doctor, not a light switch”. Despite never having seen an episode of any of the other series, and not having been aware of McCoy’s iconic line. I guess it’s just something that’s inevitable for a Star Trek doctor.
And let’s not forget “He’s dead, Jim”. (“Just like the others” optional.)
That scene with the Horta was one of my favorites. * “I’m beginning to think I can cure a rainy day.”*
Of course, my favorite McCoy line is when he mumbles to himself: If I jumped every time a light came on around here, I’d end up talking to myself.
My favorite McCoy line actually comes from an SNL skit. Kirk & Bones are at a restaurant, when suddenly a patron begins choking.
Kirk: “This lady’s choking to death. McCoy, help her!”
McCoy: “Dammit, Jim! I’m a doctor, not a… oh, right.”
Apparently (possibly apocryphal story), Robert Picardo ad-libbed the line “I’m a doctor, not a nightlight” during his audition, without being (consciously?) aware of the catchphrase, and it ended up being added to the episode script the test scene was drawn from.
My “ST:TOS in one sentence” quote has always been
“Oh, fer God’s sake, she’s DEAD, Jim!”
Huh, apparently, there’s some discussion of what Picardo* actually said. I’ve always read it as “I’m a doctor, not a light bulb.”
Never having listened to any audio commentary on VOY DVDs, I wonder if anyone has and can give a definitive answer to this trivial trivia?
*when VOY first came on TV, I liked the robert PICARDo name for my own silly Trek reasons.
Which reminds me of an interesting phenomenon. Everybody remembers those “I’m a doctor…” lines as being preceded by “Damn it, Jim!” But of course, they weren’t. McCoy (on the TV series) never said “Damn it, Jim,” if for no other reason than that you couldn’t say “Damn” in that casual way on TV in the 1960s.
They do have McCoy saying “Damn it, Jim” in the reboot movies, but that’s not the source of the meme. Rather, it’s because everyone expects that preliminary phrase to be there. If it weren’t, it would feel “wrong” to most people.
I have always been curious to know who was the first person to ever add “Damn it, Jim” when supposedly “quoting” Bones.
I don’t.
You’re going to disagree with MrAtoz on a Star Trek question? He might send you back to the past without preparing you. 
I believe that City on the Edge of Forever was the first episode that used “hell” in a non-literal manner.
Kirk: Let’s get the hell out of here.
Well, let’s say a lot of people do. Or at least I sure see it quoted that way a lot in popular culture.
Another great Picardo use of the meme is in Star Trek: First Contact. Doctor Crusher activates the Enterprise’s EMH and orders it to delay the Borg while they evacuate Sick Bay.
“I’m a doctor, not a doorstop.”
He ends up delaying the Borg by offering them medical advice.
In ST-II:TWoK, McCoy says, “Damn it, Jim! What the hell’s the matter with you? Other people have birthdays, why are we treating yours like a funeral?”
Early 80s vintage film. Lots of TOS still on TV at that time. Probably all the McCoyisms get lumped together in people’s memories.
Now, in a certain …not unfamous… episode from TOS season 1, Kirk has the last line of the ep and says, “Let’s get the hell out of here.”
.
ETA: Zephram got there first, I see.
.