This page contains information and good advice for Danes travelling to the US, including registration on the List of Danes Abroad.
For Danes wishing to travel to the US all visa applications should go through the Embassy of the United States in Copenhagen, Denmark.
If you are travelling to the US for tourism and/or business you might not need a visa due to the Visa Waiver Program. Instead you have to apply for an Electronic System for Travel Authorization (ESTA): an online application system that tells you if you need a visa or if you can travel under the Visa Waiver Program.
Read more about visa requiremtns and applications to the US at the Embassy of the United States in Denmark's website: http://denmark.usembassy.gov/non-immigrant_visas.html.
Specifically on the Visa Waiver Program and ESTA: http://denmark.usembassy.gov/non-immigrant_visas/visa-or-esta-.html.
Read more on the Ministry of Foreign Affairs' website: http://um.dk/da/rejse-og-ophold/rejse-til-udlandet/pas-og-visum/usa-pas-og-visum/.