Resources

Ordnet.dk
Danish-to-Danish dictionary
*Includes links to audio pronunciation of words *Provides all grammar info (tenses, plurals, etc)
*Gives multiple uses for words and phrases
*Shows origins/history of words 
Study Danish at a great university!
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Excellent program in Danish language and literature taught by outstanding professors who foster quality research and skilled teaching in their students.
Click here for other US universities offering Danish programs!
Podcast/Blog from Kay Xander Mellish detailing life in Denmark, tips about Danish business culture, and much more
"Danmarks Radio" is a radio/tv/news source and also contains videos (some in English with Danish subtitles, some in Danish - there is usually a subtitle button, so you can listen to the Danish and see the Danish words).  Most can be seen while in the US, but some are blocked due to broadcast agreements and contracts.  Live tv is also available at this website. 
Danish news in English
Danish Radio/TV
Hjælp til danske forældre i udlandet
Denne webside er til danske forældre, der bor i udlandet, og gerne vil lære deres børn dansk.  Find alle mulige svar og informationer her:
Click on the link above for information regarding short-term, long-term stays in Denmark, resident and work permits, and so on.
US citizens do not need a visa if they are entering the Schengen area as a tourist for 90 days or less