The Danish Agency for Culture maintains a register of buildings in Denmark, including approx. 9,000 listed buildings. The register is in Danish only. You find it here: Danish Buildings.
Many local authorities have registered buildings from before 1940 using the SAVE (Survey of Architectural Values in the Environment) method. This nationwide registration of about 400,000 buildings is available on the Internet, too. Read more about the SAVE method (publication) here.