Related to YMMV, except these particular fan-reactions and interpretations are quite widely entrenched in fannish thought.
A very popular bit of fanon in the Sherlock Holmes fandom is that Dr. Watson's middle name is Hamish; this theory was first devised by Dorothy L. Sayers in order to explain why Watson's wife calls him James in one story although his first name was previously stated to be John (Hamish is the Scottish form of James).
This happens quite a bit in Sherlock Holmes. Among other things, it's fairly established fanon that Holmes' parents were called Violet and Sanger, he at some point was part of a Shakespearean acting troupe that toured America, his older brother Mycroft is head of the proto British secret service, and the eldest of the Holmes brothers is called Sherringford (the name Arthur Conan Doyle gave to Sherlock in early drafts), a country squire.
More Sherlock Holmes fanon; Watson had three wives, Holmes and Irene Adler met in Montenegro while he was faking his death between The Final Problem and The Empty House and fathered a child who would grow up to be Nero Wolfe, that the King of Bohemia was Edward VII, that Holmes worked on the Jack the Ripper case (and it was Watson who secretly solved it), that Holmes's retirement to bee-keeping was in the hope of creating "royal jelly" (believed then to be a sort of Fountain of Youth) and that Holmes spent the last decade of his life fighting Nazis before dying at the ripe old age of 90. All of this is present in W.S. Baring-Gould's tongue-in-cheek "biography", Sherlock Holmes on Baker Street.
A mostly irrelevant Epileptic Tree refers to Watson's bulldog, which is mentioned in A Study in Scarlet when Holmes and Watson first meet and move in together and then completely disappears. The theory varies, saying that Holmes either used the dog for an experiment that resulted in its death, or, the more PETA-friendly version, he simply had Watson get rid of it.
For some reason there's a train of thought in parts of the fandom that either Sherlock or Watson (most commonly the former) are Female-to-Male Transsexuals.
People who join the 'Baker Street Irregulars" have to write an essay. Rex Stout's was titled "Watson Is a Woman".
Many adaptations talking about Sherlock's family-life (Young Sherlock Holmes, The Seven Percent Solution, Sherlock) seem to be oddly agreed on the fact that a young Sherlock Holmes deduced that his father was having an affair, told his mother and ended up ruining the family.
For some reason, Holmes/Watson is so widespread, it's often mistaken for actual Canon by fandom newbies. Adaptations don't help. Is considered Serious Business by some fans to the point essays are written about the "subtext". (In a series where "ejaculation" means "sudden exclamation" and nothing else, at that.)
Watson's appearance is never described beyond being "brown as a nut and thin as a lath" in A Study in Scarlet, and that after having just returned from severe illness abroad. Later, Watson's describtion was given as " middle-sized, strongly-built, square jaw, thick neck, and mustached." Nowadays, though, it's generally accepted that he was blond - helped along, perhaps, by David Burke of the Granada series and Vitaly Solomin of the Russian series, not to mention Jude Law and Martin Freeman.
Another piece of Fanon that's spreading is the given name "Geoffrey" for Inspector G. Lestrade. This originated with Marcia Wilson and has been picked up by an unknown number of fans, including Aleine Skyfire and Riandra.