Sherlock Holmes is a character that most people either love or hate; there is not often a middle ground (except, of course, for those who haven't read any of Conan Doyle's detective works at all). Hating him would be perfectly understandable, judging from his cool arrogance, his occasional petulance, and his scorn for those without minds like his own. He goes through highs and lows like a roller-coaster, spending his days, when he is without a case, either sulking with his long-stemmed pipe or sprawled out on the sofa in a daze, probably narcotic-induced. He apparently has little regard for anyone. He lives, generally speaking, in his own little world.
With a description like that, it seems a wonder that anyone likes him. Yet the fact that people do means that there is something more to Holmes than this, or that Conan Doyle managed to write such an egotistical character with charm. In reading Holmes, I found it was both.
This is not to say that anything in my description of Holmes is wrong; he is, by turns, arrogant, petulant, and scornful, and no mistake. But he is not merely all these things, else he would not have become nearly as popular as he did. For one thing, though his arrogance can be a little grating, one does at least have to concede that he is not conceited without reason; he is not like Inspector Lestrade, who preens over having solved a crime, while nabbing the wrong fellow. He is a genius, and keenly aware of the fact. However, Holmes is not without his failures, and not above being disgusted with himself when he overlooks a clue or finds himself (as he does, albeit rarely) stumped. There is a limit to his conceit.
"'Watson,' said he, 'if it should ever strike you that I am getting a little overconfident in my powers, or giving less pains to a case than it deserves, kindly whisper "Norbury" in my ear, and I shall be infinitely obliged to you.'" (The Memoirs of Sherlock Holmes: The Yellow Face.)As for his petulance during times when he is without a case, the very childishness that on the one hand can make his behavior irritating can also make it endearing. Holmes is very much like a child in some respects - quick either to fling himself wholeheartedly into work, or to give up all pretense of labor; ascending rapidly to the pinnacle of delight, and plunging again two seconds later into Anne Shirley's "Depths of Despair." These wild mood swings are amusing to watch, and it is always satisfying to watch him bound back out of his dejection with the arrival of a new, challenging case.
His scorn for Scotland Yard is also understandable, as Conan Doyle surrounds him with inspectors like Gregson and Lestrade, who are occasionally effective, usually blundering, and always looking down their noses at Holmes' "methods" until the last minute. Coming to Holmes is always their last resort, and though he always manages to solve the case for them, they then kindly inform him that they will "make something of him yet." Yet Holmes is generally good-natured about allowing them to take the credit for problems he has solved, and rarely asks for more than the enjoyment a case provides for him.
Besides these points, Conan Doyle's major weapon for making Sherlock Holmes likable is the fact that the story is told, not from the detective's point of view, but through the first-person narration of Dr. Watson. However, Watson deserves a post of his very own, so I will enlarge on that later.