I lived in Denmark for two years and it is arguably the most Americanized of European countries (saving Netherlands, perhaps). I’ll give you the rundown on the extent of the “damage”
Television: Majority of programming is in English with Danish subtitles. I’d say it’s at least 60 percent english-speaking if not more. Vastly more American stuff than English, except for soccer. Oh, also, American football is becoming a big deal in Denmark. Many Danes are interested in this.
Movies: As you might guess, movies are even more exaggerated. At any given moment 80 percent of the movies will be American. For a country of 5 million people, they do produce a lot of quality films, and a significant amount as well, but they simply can’t compete in terms of sheer quality. They are always in English, unless it’s an American kids movie, which would be dubbed. The Danish movies are obviously in Danish.
Food: This is an area where Americanization hasn’t really made a huge dent. Sure you can get hamburgers in loads of places, but they aren’t really hamburgers after the Danes get done with them! Probably similar to the transformation that a cream-cheese Danish underwent to come to America. As far as fast food is concerned, Copenhagen doesn’t have so many McDonalds or other things. It isn’t like in other European capital cities that I’ve been to. Stroget (the main area of town) has three, all within 10 minutes walking, but once you get outside of the center of town and to the other areas, they become less common.
Also, McDonalds seems to be a class thing. I normally only see more working-class kids eating there. It’s very popular with teenagers but not so much with older folks. Starbucks doesn’t exist in DK (Yes! it’s true!). Or at least I’ve never seen one. I’ve been around that country quite a bit too.
There’s a few Burger Kings and a KFC there too.
But I think food is probably the least likely area in which anything is to ever make a difference. People learn to have certain tastes as children, which is the point when your parents are usually going to be cooking traditional-type foods. American food is no more popular than Italian or Turkish, etc.
Music. This is really interesting in that American music is probably less popular in Denmark than in most places. Obviously there are different types of genres, but there is a thriving Danish music scene with a lot of great bands. Of course people will listen to international bands, but really there’s no threat of that displacing the Danish stuff.
What you will see a lot of in Denmark is Danes appropriating “American” stuff. Rap has really gotten huge in Denmark. This would be by Danish artists too.
The funny thing about Denmark is that it is very open to these new things, but at the same time very insular. I wouldn’t say that the Danes are protective of their culture so much as they are really just fond of it. They find it so hygge that they wouldn’t understand not liking Danish things.