StatBank Denmark contains detailed statistical information on the Danish society.
The database is free of charge and data can be exported in several file formats and presented as diagrams or maps.
Population and elections
Education and culture
Social conditions, health and justice
Income, consumption and prices
General economic statistics
Construction and housing
Environment and energy
National accounts, balance of payments and international investment position
Money and capital market
Seems as though its open as long as source is acknowledged. Notice says:
When making use of the material submitted Statistics Denmark - statbank.dk or other data supplier shall be stated as the source in accordance with established custom and to the extent conditioned by the purpose.