As an American in Denmark, I get to experience Danish stereotypes about Americans on a regular basis: we are superficial, too outspoken and direct, and are apparently controlled by a small cabal of right-wing nutcases. 
But the Danes have stereotypes about other nationalities as well.  Spaniards and Italians are seen as fun and sexy and romantic, but unlikely to arrive on time. Eastern Europeans work too hard, at wages that are much too low, at least by Danish standards. Asian immigrants are seen as OK because they work hard at things Danes aren’t interested in, like high-level engineering degrees.

Danes also have stereotypes about other Nordic people. Norwegians are seen as happy, friendly people with a humorous language.  Everything sounds funny in Norwegian because everything sounds like singing.  Swedes are seen as kind of stiff, humorless types who can’t dance, and can’t hold their liquour.  Finns are silent, angry drunks that carry knives. Oddly, given their history, Danes really like Germans.  Really, really like the Germans.  Many Danes will say that Berlin is their favorite town.
Danes also have stereotypes about each other, something that amazed me when I first arrived here.  You have 5 million people, and you’re dividing yourselves into groups!  But Danes themselves see a big difference between people from Sjelland, the island with Copenhagen on it, and Jylland, the bigger part of Denmark that is connected to Germany.
As the stereotype goes, people from Jylland are seen as quiet, reliable, trustworthy, and likely to marry young and start families. They are also sometimes seen as stubborn, and very tight with money. They want to drive a hard bargain. People from Copenhagen are seen as slick. Smart-ass, fast-talking, prone to exaggeration- everything’s the biggest and the best.  The men wear expensive business suits, and everyone wears overpriced eyeglasses. They have jobs that are non-jobs, like Senior Communications Consultant or SEO specialist.  People from Jylland have real jobs, like pig farmer, or Lego designer.