Elementary

Elementary, my dear Watson“, sometimes quoted as, “Elementary, dear Watson“, is one of those phrases that everybody knows the character of Sherlock Holmes said. The thing is, Holmes never said “Elementary my dear Watson” in any of the original 56 short stories or 4 novels starring his character. The closest he comes is in, The Adventure of the Crooked Man.
In this story, Holmes uses both the word “Elementary” and the phrase, “my dear Watson“, in somewhat close proximity. The two, however, are not uttered together:

“I have the advantage of knowing your habits, my dear Watson,” said he. “When your round is a short one you walk, and when it is a long one you use a hansom. As I perceive that your boots, although used, are by no means dirty, I cannot doubt that you are at present busy enough to justify the hansom.”
“Excellent!” I cried.
Elementary,” said he.

Beyond that, there are only 7 other instances of the word “elementary” being uttered in the official Sherlock Holmes works, though he does say “my dear Watson” numerous times, with the phrase appearing in about 2/3 of the stories, sometimes several times within a given story.
It’s noted by Sherlockian.net, one of the foremost sources on everything to do with Sherlock Holmes, that although Holmes never uses the misquoted phrase, “elementary, my dear Watson“, he does use the phrase, “exactly, my dear Watson” in 3 different stories. For example in His Last Bow, where Holmes uses the phrase in a shoddy attempt to mask the obvious tension between himself and his man servant… Or, you know, to agree to Watson’s point.