You know your hobby is more than a hobby when the general public is interested. The fact that 221B Baker Street has been receiving letters since Conan Doyle's time and that children today still ask the same question is testament to the longevity and realism of Sherlock Holmes.
The Straight Dope, a myth-busting website whose motto is "Fighting Ingorance Since 1973 (It's taking longer than we thought)" published this question on April 8, 2008:
Did Sherlock Holmes really exist?
The author goes on to answer the question in great detail, examining how the stories came about and the cult that grew around them, including the seminal work on Sherlockian scholarship, Father Ronald Knox's "Studies in the Literature of Sherlock Holmes," which is embedded here for your benefit. Feel free to browse, download, print or otherwise share this document.
Along the way the columnis heartily recommends some reading, namely: The Complete Sherlock Holmes, which contains all of the original Canonical stories and The Annotated Sherlock Holmes by William S. Baring Gould. Of course, these days, we'd recommend The New Annotated Sherlock Holmes by Leslie Klinger instead.
Feel free to make some of these selections below from Amazon - make it a very Sherlockian Christmas or other winter holiday for yourself or those you love.
What are those four-letter abbreviations in the headlines?