Fun site - be sure to stop and read each 'segment' of the walk. The Round Tower has a great view but it's history is more impressive.
Definitely worth going to. The price is a little steep for what it is, but you get some great views of Copenhagen when you are at the top.
Originally built as an observatory, this is one of the most visited sights in Copenhagen with good reason. The main feature is the incredible internal spiral ramp leading to the top, built so that horses could be ridden all the way to the top. The views once you reach the top across the city are worth the trek and each floor usually has an exhibition space or an arts and craft market.
Great view from the top over the whole city.Very nice!