I am an Norwegian. On an 1 to 10 scale i would put Sweden on 8 on how good i understand them. However, whenever i listen to a Dane i have to focus a lot more. It just sounds nothing at all similar. Is the Dane language even from the same branch as the other norse countries?
This is more of a question for /r/linguistics, another great sub.
They are all three parth of the north germanic languages, but Norweigen comes from West Norse, while Swedish and Danish both comes from East Norse. So all three languages come from Norse and historical Swedish and Danish is closest to each other. Up through history Danish have changed differently than the other two languages.
Danish have more words taken from Low German than Swedish or Norweigan. A good example is "eat", which is "spise" in danish and "äte" in Swedish. Danish still keep the old word, "æde", but now it only refferes to animals eating.
Then there is the vowel shift. Most germanic languages underwent some kind of vowel shift from 1200-1700. The exact time it happened depends on the country, but in english it happened from 1350 to 1700 and is called "The great vowel shift". In Sweden and Norway this affected the back vowels, but in Denmark it affected the front vowels and danish got its infamous "stød"
Stød is a part of danish phonology and is not found the same way in Swedish or Norweigan. Here is a small video where you can hear words without and with stød. First part is some explanation in danish, but the interresting part starts at 1:50. The first word in a line is without stød and the second word is with stød.
http://m.youtube.com/watch?v=OmDZggqBudc
Edit: big changed to great. Thanks for the correction MooseFlyer