Recently, Wayne Manor has been taken by the mayor, via eminent domain, in order to contain Gotham's criminally insane who's previous home was destroyed. It has been converted into an operational prison and is now known as "Arkham Manor".
Wayne Manor was located in Bristol Township, twelve miles away from Gotham City. Further from Gotham there were caverns and tunnels that were sometimes referred to as the Catacombs. Bruce Wayne often played within these caverns before his parents demise. The Manor was designed by Nathan Van Derm for Darius Wayne in 1795.
The main use of the tunnels were to free slaves from the south and send them up the east coast and onto Canada. Each generation of the Wayne family lived in the manor and it's remained one of the finest buildings in Gotham, until it was destroyed by a massive earthquake during the " Cataclysm" arc. It was subsequently rebuilt from scratch by Bruce Wayne choosing to be inspired by Cyrus Pinkney, Gotham's original architect, thus giving Wayne Manor its Gothic design.
The new manor was designed not only with economics but security in mind to protect Bruce Wayne and the Dark Knight's identity. The new structure still maintained the traditional grandfather clock that, by setting the hands to 10:48, the time of his parents' deaths, allowed Bruce Wayne access to the Batcave. Alfred is responsible for maintaining Wayne Manor.
Recently Alfred, Dick and Damian have discovered new rooms with clues left by Bruce Wayne during his travels in time, which started after Darkseid shot him with the Omega Effect during the Final Crisis. For example Dick found a secret room that is not on the original plans of the manor, this room has the word Barbatos written in big letters and the name Thomas written many times in smaller letters. The new batman also noted the paint was a year old tops and it should be from the 18th century had it been written by Thomas Wayne, the devil worshipper. This room contained another secret passage which let to the catacombs were Dick found a stalactite carved to look like a half human, half bat person. This sculpture is Barbatos, the devil-bat of the Miagani tribe who was summoned by Thomas Wayne. Not long after Dick discovered the Barbatos sculpture the cape and cowl that Bruce used against Darkseid appeared as if it were and altar.
Wayne Manor appears in the 60's Batman series. Like in every other depiction, the house was above the Bat-Cave which could be entered by pressing a button placed in a model of William Shakespeare that caused a bookshelf to slide away and reveal the secret passage.
Batman: The Animated Series
In Batman: The Animated Series, Wayne Manor was given the address of 1007 Mountain Drive which was located on a cliff above the ocean and, when seen from a certain angle, looked like a pair of pointed bat ears.
The manor is seen in the new series, Gotham. Bruce and Alfred reside here and James Gordon has visited the house numerous times.
The Nolan Trilogy
Wayne Manor appears the Christopher Nolan's interpretation of Batman. In Batman Begins, the house is burnt down by Ra's al Ghul but its foundations survive and, at the end of the film, Bruce plans on repairing his home. The house is, however, not seen in The Dark Knight due to the fact that it's still under construction. By The Dark Knight Rises, the house is complete and Bruce is seen living here with Alfred once again. At the end of the film, half of Wayne Manor is converted into an orphanage and the other is given to Alfred.