The site www.woco.dk - "Wonderful Copenhagen" - claims to be the official tourist site of Copenhagen. In reality, this means that it is operated by the tourism business. This should be kept in mind when reading its appraisal of some Copenhagen sites - whether they are commercial or not. The site is professionally designed and entirely in English. Furthermore, it is updated on a regular level with the biggest news and events in the Copenhagen area. Its content, however, seem to be mainly targetted on the busy business traveller with just a few hours to spare, rather than the full time city tourist.
The Danish Ministry of Foreign Affairs is the public authority behind www.denmark.dk, an English language web site that provides a lot of good, factual information about Denmark in general. It is particularly useful for foreigners planning a longer work or study related period in Copenhagen (or the rest of Denmark).
With a highly professional look and content in several languages, the www.visitdenmark.com site of the National Tourist Council is a rich source of information about sights and events throughout Denmark, including Copenhagen.
The useit.dk site is a service from the municipality of Copenhagen with information provided especially for the low budget traveller (typically students). Whereas it probably cannot provide information an all you may want to know, it is certainly worth a look if you are a member of the target group.
The highest update frequency, you find at www.aok.dk - "Everything About Copenhagen". It is the preferred "What's happening in town tonight?" source of information to many Danes. Even though the site is primarily intended for the local - Danish speaking - audience, it does have some English language content. Here you can find information about restaurants, concerts, movies, events etc.