The question was promptly seconded by Marian, and yet I've managed to avoid writing up an answer for a few months now. Mainly because I didn't have an answer.
I've read all of the stories multiple times and yet I have trouble picking out a favorite. It could have something to do with the fact that I love them all so much. Or that I haven't read any Sherlock since the summer, so they blend together in my memory as being one long, mysterious and wonderful tale.
However, when I think about the ones that gave me chills (all of them) or nearly made me cry (several of them) one short story stands out to me as being particularly memorable. It is the only story where Sherlock loses his icy composure for one brief moment and lets the audience get a glimpse at his feelings.
And I am not talking about the story with Irene Adler, The Woman. Yes, she was the only woman who ever bested Sherlock and he had a great deal of respect for her, but he was not in love with her.
The story I'm referring to is The Three Garridebs, and here is the passage I love. Holmes and Watson are on a stakeout, and shots have just been fired.
I felt a sudden hot sear as if a red-hot iron had been pressed to my thigh. There was a crash as Holmes's pistol came down on the man's head. I had a vision of him sprawling upon the floor with blood running down his face while Holmes rummaged him for weapons. Then my friend's wiry arms were round me, and he was leading me to a chair.This display of feeling for his friend disproves Watson's previous judgement of Holmes."He was, I take it, the most perfect reasoning and observing machine that the world has seen..." Before Watson really gets to know Sherlock, he believes him to be cold and calculating, a brain without a heart. That is simply not true. Sherlock Holmes knows how to master his emotions and let logic win over feelings, but that doesn't mean that he never feels at all.
"You're not hurt, Watson? For God's sake, say that you are not hurt!"
It was worth a wound - it was worth many wounds - to know the depth of loyalty and love which lay behind that cold mask. The clear, hard eyes were dimmed for a moment, and the firm lips were shaking. For the one and only time I caught a glimpse of a great heart as well as of a great brain. All my years of humble but single-minded service culminated in that moment of revelation.
"It's nothing, Holmes. It's a mere scratch."
He had ripped up my trousers with his pocket-knife.
"You are right," he cried with an immense sigh of relief. "It is quite superficial." His face set like flint as he glared at our prisoner, who was sitting up with a dazed face. "By the Lord, it is as well for you. If you had killed Watson, you would not have got out of this room alive. Now, sir, what have you to say for yourself?"
I like this story because it shows that Sherlock Holmes is human.