Miklos Rozsa wrote a wonderful score for a film called The Private Life of Sherlock Holmes. Here is a suite from that score:
A nice contrast is this score by an underrated and underused composer named Bruce Broughton, for the film Young Sherlock Holmes. I always had a difficult time with this film, owing to its odd conversion of Holmes into an Indiana Jones-like adventurer and its somewhat downbeat ending. The music, though, is quite good.
And then there's the BBC's theme, which is incredibly earwormy:
By the way, my personal favorite portrayal of Sherlock Holmes came in an episode of Magnum PI, in which Patrick Macnee plays a friend of Higgins's who has gone delusional to the point of believing himself to be Holmes. It's a really good episode, called "Holmes is Where the Heart Is". Worth checking out, if you have access to the show...I believe it's on Netflix.
The game's afoot, folks!