My neighbor already had a wooden privacy fence up. New neighbor's bought the home and put up a new privacy fence w/o taking down the old one. Basically a double privacy fence. Is that legal?
As Alan Ward says, it depends on your local jurisdiction.
In the UK, for example, it would be perfectly legal as long as it is on their land - in fact it is quite common in certain circumstances, for example if someone lives next to an industrial unit with a big metal security fence, they might put up a nicer-looking wooden one to hide the unsightly metal one.