Cheap Youth Fare, Scandinavia Airpass with SAS
SAS http://www.flysas.com, the airline that connects Denmark, Sweden and Norway with other parts of the world, offers one-way fares to the U.S. to those under 26 years of age for less than $200. According to a post on http://www.flyertalk.com, this is in addition to youth fares they have for places such as Asia, a favourite winter destination for descendents of the Vikings. It is also possible that your age will not be verified if you look less than 26 (or can alter your documents to show that you are.)
Scandinavia is an expensive part of the world, so if you plan extensive travel there it could be worth looking into a Scandinavia Airpass provided to foreigners by the same airline. I couldn't locate the details quickly, but with work I am sure it is possible to find it on the Website. Sweden and Norway are largish countries, so air may be the most efficient and cheapest way to get around.