There are Go clubs in Aarhus ( old page), København, Odense, Ringsted (Ringsted Go Klub, Medborgerhuset, Søgade 3; kontakt: Peter Andersen, 5752 7292), Sønderborg (Kjeld Petersen).
The Copenhagen page has some more information, such as a list of national champions, and results of past tournaments.
See also the pages of Kasper Hornbæk and Stina Pedersen (and don't click on the link that says "don't click here"!).
The Copenhagen Open 2000 tournament was held September 30th - October 1st.
The Danish national championship 2001 was held May 11-13 in Odense.
Elsewhere one can find information on other countries.