Which fictional detective lives at 221B Baker Street?

Sherlock Holmes, at an address that did not exist when Conan Doyle invented it. Baker Street numbers only ran into the 80s in the 1880s; the street was extended in the 1930s and the number came into being, whereupon the building society that occupied it received so much post addressed to Holmes that it employed someone specifically to answer it.

That correspondence is the interesting part. People wrote asking for help with real problems, apparently believing or half-believing he was real, and the letters continued for decades. There was a long dispute between the building society and a later Sherlock Holmes museum nearby over who was entitled to the number, which Westminster council eventually resolved by allowing the museum to use 221B although it physically sits between 237 and 241.

Holmes is now the most-portrayed literary character in film and television, with several hundred actors in the role. He is also why several things people assume are canonical are not: he never says elementary, my dear Watson in any of the stories, and the deerstalker and curved pipe come from illustrations and stage productions rather than from Conan Doyle, who put him in a soft cloth cap and a straight pipe.