On Wallander they always speak Swedish and the Danes usually speak very basic, thickly accented Swedish. But I have very good Danish and Swedish friends and they just talk with each other in their own languages and get on fine. Some Swedish people I know say that they can't tell the difference between Danish and Norwegian (Bokmal) speaker, which I find a bit strange.
Calling Dayvo for the definitive answer, I think!
OK,
you asked for it I'll do my best!
In a nutshell, Danish, Norwegian and Swedish (and Icelandic) stem from the same language
Old Norse. On becoming seperate kingdoms their languages evolved differently.
Generally speaking, Danes, Norwegians and Swedes will inderstand each other in the same way an Englishman, Scotsman, Welshman and Irishman will.
However, with strong heavy regional accents, understanding becomes more difficult: imagine a Cornishman, Brummie, Scouser, Geordie, Glaswegian, a Welshman (with English as his 2nd language) and a Kerryman having a conversation! A similar situation will arise within Scandinavia.
If anything, Icelandic is pure Norwegian (as Norway had 434 years of Danish rule, then 95 years under Swedish rule) as the island was settled by Norwegians over 1,200 years ago.
The difference is not as close as the British dialects and accents, but closer than Spanish, French and Italian, and more like German German, Swiss German and Austrian German.
And breathe!