Sarah C. Rich wonders where he got it:
Sherlock’s unmistakeable deerstalker hat…was never mentioned in the printed words of the Holmes books. When Sidney Paget illustrated Doyle’s story, The Boscombe Valley Mystery, for publication in The Strand Magazine in 1891, he gave Sherlock a deerstalker hat and an Inverness cape, and the look was forevermore a must for distinguished detectives—so much so that while the deerstalker was originally meant to be worn by hunters (hence the name), the hat now connotes detective work, even without a detective’s head inside it. Of course, as many Sherlockians know, the deerstalker wouldn’t have been Holmes’s daily choice of headwear. These hats were country gear, not fit for the city.
Update from a reader:
A couple more bits regarding the hat: a clip from BBC's "Sherlock". An article regarding the hat in the above installment of "Sherlock." Money quote:
The deerstalker hat – a feature of Sidney Paget’s illustrations, as all Holmesians know, rather than Conan Doyle’s text – is similarly treated as an in-joke in the TV version: an impromptu shot of Sherlock in a borrowed deerstalker becomes the stock Press image, much to his irritation.
(Illustration by Paget)
The Dish 