Elementary is a contemporary update of Sir Arthur Conan Doyle's character Sherlock Holmes, starring Jonny Lee Miller as Sherlock Holmes and Lucy Liu as Dr. Joan Watson, a female version of Holmes' companion. Here, Holmes is a former consultant to Scotland Yard and a recovering drug addict. He travels to New York City to check into a rehabilitation center and then lives with Watson, who becomes his sober companion and eventually his apprentice.
Either these shows spun from great books (many of which I read first!) or are based on well-known literary works, often with a modern spin. I exclude gothic novels and comics from this list since I have a list for that lol.