"The Adventure of the Speckled Band," "The Red-Headed League," and "Scandal in Bohemia" are my favorite Sherlock Holmes short stories. The Speckled Band is by far and away the best of the shorter stories.
Out of all the collective Sherlock Holmes' stories and novels, my all-time favorite would be The Hound of the Baskervilles for its eerie supernatural elements and suspense, and of course, any story featuring that "Napoleon of Crime," the sinister Dr. Moriarty.
I would have to agree with the above and add the following: "The Case of Identity" and "The Five Orange Pips." The top five stories would be hard to universally name given readers different likes and dislikes vary so much.
I would go with The 'Hound of the Baskervilles' and 'A Study in Scarlet' to add to those mentioned above. My favourite would be the Speckled Band due to its clever construction of evidence.
Hmmm.... kind of hard to say. I think I'd go with a top three (looking only at short stories) of "The Man With the Twisted Lip," "The Adventure of the Red Headed League" and "The Adventure of the Speckled Band." I can't say that those are objectively better than the others, but they are three of my favorites.