This comes up from time to time. When we think of Sherlock Holmes we immediately think of the phrase, "Elementary, Watson." Or even, "Elementary, my dear Watson." This phrase never actually occurs in Conan Doyle's (wonderful) stories of the adventures of Sherlock Holmes. It's easy to download the complete canon and search through it:

grep  -A2 -B2 -i elementary holmes.txt 

     Before turning to those moral and mental aspects of the matter which
     present the greatest difficulties, let the enquirer begin by
     mastering more elementary problems. Let him, on meeting a
     fellow-mortal, learn at a glance to distinguish the history of the
     man, and the trade or profession to which he belongs. Puerile as such
     hurry and dipped her pen too deep. It must have been this morning, or
     the mark would not remain clear upon the finger. All this is amusing,
     though rather elementary, but I must go back to business, Watson.
     Would you mind reading me the advertised description of Mr. Hosmer
     "Excellent!" I cried.

     "Elementary," said he.  "It is one of those instances where the
     reasoner can produce an effect which seems remarkable to his
     neighbor, because the latter has missed the one little point which is
     looked over it again with a convex lens.

     "Interesting, though elementary," said he as he returned to his
     favourite corner of the settee. "There are certainly one or two
     indications upon the stick. It gives us the basis for several
     bourgeois type of a Times article and the slovenly print of an
     evening half-penny paper as there could be between your negro and
     your Esquimau. The detection of types is one of the most elementary
     branches of knowledge to the special expert in crime, though I
     confess that once when I was very young I confused the Leeds Mercury
     he remarked. "It is very pleasant to see the first green shoots upon
     the hedges and the catkins on the hazels once again. With a spud, a
     tin box, and an elementary book on botany, there are instructive days
     to be spent." He prowled about with this equipment himself, but it
     was a poor show of plants which he would bring back of an evening.

     "The train of reasoning is not very obscure, Watson," said Holmes
     with a mischievous twinkle. "It belongs to the same elementary class
     of deduction which I should illustrate if I were to ask you who
     shared your cab in your drive this morning."
     as the astute reader will have already perceived, few difficulties in
     its solution, for a very limited choice of alternatives must get to
     the root of the matter. Still, elementary as it was, there were
     points of interest and novelty about it which may excuse my placing
     it upon record. I now proceeded, using my familiar method of logical

So, there are eight appearances of the word "elementary" and only one of them is written in the same sense as the famous cliche. It's fascinating how these memes establish themselves.

[Edit 2012-07-30: Apparently another of my favourite authors, P.G. Wodehouse, may be responsible for the phrase. It appears in "Psmith, Journalist", published in 1915.

"Elementary, my dear Watson, elementary," murmured Psmith.

Wonderful! ]