Symbol of the town, it's part of the castle remains. Built in a seven storeys rounded shape by Waldmar IV in 1366, it's famous for its golden goose at the top.
The Royal Castle was built in the 12th century by Valdemar the Great. He built the castle close to the coast to make it a good harbour for his fleet, that was fighting the Wends at that time. Valdemar the Victorious extended the castle and it was Valdemar Atterdag, which means 'day again', who built the outer wall and four big watchtowers, of which only the Goose Tower is still standing.
The Goose Tower was part of the fortifications at Vordingborg and the access to the watchman's gallery, on top of the stone wall, is still visible now.
The Goose Tower got it's name because of the goose that was placed on top of it by Valdemar Atterdag, to scorn the Hanseatic cities, who cackled like gooses. The present goose is from 1871 by the way.
The museum of south zealand exhibits the history of the town of Vordingborg from as early as the Stone Age up to the 20th century. The construction and development of Vordingborg castle is the most interesting part of the collection. If you want to know more about Stone Age, viking age or middle age, it's probably nicer to visit the National Museum in Copenhagen.
Maybe it was a temporary exhibition, but the museum also showed old insects, captured in the 'gold of the north', the thick, orange juice from trees that turns solid after some time (sorry I don't know the English name).