Apart from some regional peculiarities (mostly rotten fish), the Scandinavian kitchens aren't that different, by the way.
One thing that Denmark has, that I am sure that the Norwegians and Swedes must be envious of, is proper beer. I have spent many summers in Norway and Sweden during my childhood and youth, and I have come to find that Swedes and Norwegians make boring beer. I'm not even a particularly big fan of Carlsberg, Tuborg, etc., but I simply cannot drink another Blå Pripps in my life.
My favourite Danish dish: Nothing and a glass of Gammel Dansk ("Old Danish"), a spicy bitter schnaps. According to the English Wiki article on it, it is drunk in the morning with the breakfast, which I have never heard about anyone doing, but hey, maybe I should try that.
Other Danish classics: Karrysild, curry herrings on rugbrød, dark rye bread. Sided by the eternally shining star that is Rød Ålborg, the Danish equivalent of vodka.