Who colonized Denmark?

Answer 1

Denmark proper (including Baltic sea island of Borkholm) by Germany 1940.

Faroe islands by Great Britain 1940 (few days later to prevent German invasion)

Greenland was not occupied, but German special forces (there to set up a weather station) was fought off with US assistance.

Bornholm 1945 by the Soviet Union, who only left after almost a year.

Answer 2

The core of the population of the area called Denmark has been the same for at least 5.000 years (which is not the same as saying that it is homogeneous, which is not the case), and there has never been a colonisation by a foreign power [...but many cases of inflow of foreign people through the ages like Slavonic tribes, Germans, French Huguenots, Jews, fellow Scandinavians, Poles, Yugoslavs, Turks and in recent times Pakistani, Lebanese, Iraqi and Somali refuges]

If the question should be understood as 'Who was colonised by Denmark?' then the main areas would be:

England ('Danelagen') and Normandy in the Viking age.

Tranquebar in India in the 17th - 19th century.

Several forts on the 'Golden coast' in present day Ghana in 17th to 19th century

Virgin Islands in the Caribbean in the 18th - 19th century.

The possessions in Africa and the Caribbean was used as two "legs" in a slave trade "triangle".

In the early medieval period Denmark lead a number of crusades "against" Baltic and Slavonic pagans allegedly to convert them to Christianity. As a result Estonia belonged to the Danish king for 200 years, but it didn't lead to any permanent settlement and thus does not constitute colonisation, I guess.

You could say that Greenland was a Danish colony until 1953 (when it became a self-governing part of Denmark) but it was not colonised by Danes - it was settled by ethnic Norwegian via Iceland [who dies out in the 15th century]. Similarly, some would include other North-atlantic possessions, Iceland, Faroe Islands and the Shetland & Orkney Islands, which was originally taken over from Norway in a period, where Denmark and Norway was a single kingdom (in fact single country from 1536 to 1814).