These shows may have some stuff that could seem to fit under sci-fi, quirky, fantasy, weird, mysterious, or possibly other genres. The basic criterion for putting a show in this category is that it has, as a central element, something which is outside the bounds of everyday life (monsters, psychic powers, etc.), but which is set presumably in an otherwise normal world. I guess. Though some worlds may obviously be more realistic than others.
See also horror shows, kid stuff (under "sci-fi/fantasy"), supernatural & paranormal movies, supernatural & horror webseries, and horror/supernatural books