After seeing many film and tv adaptations and finally reading the source material, I have made one conclusion: Sherlock Holmes and John (or James) Watson are madly in love. Their connection is quickly made and strengthened by their work together.

Watson is complimentary to Holmes from the very first and Sherlock is visibly affected by his admiration.

My companion flushed up with pleasure at my words, and the earnest way in which I uttered them. I had already observed that he was as sensitive to flattery on the score of his art as any girl could be of her beauty.

Their mutual regard only deepens as the story moves toward the resolution. Watson is very observant of Holmes' expressions and moods, moreso than any standard flatmate would be after such a short acquaintance.