Ready to co-own
A popular way to live in Denmark is by partly owning. Co-owning in a housing cooperative is specially in big cities such as Copenhagen popular. One buys and therefore owns part of the apartment and you also have to pay rent, but less than usual. Besides this it also allows younger people to own their bit of real estate.
In and around Copenhagen
Around Copenhagen it might make sense to make a quick search for co-operative housing Copenhagen, co-operative housing for sale or cooperative housing in Frederiksberg or potentially even co-operative housing Amager. Going out of Copenhagen one could also search for co-operative residence in Roskilde.
Co-operative housing in Jylland
Or if the other side of Denmark is better suited for your wished then you should look in the biggest cities. Search for co-operative housing in Aalborg, co-operative housing in Aarhus or co-operative housing in Horsens.
Good luck with finding your Andelsbolig!