As I understand it, the reason the Dutch speak English so well is that a lot of American television is shown there...still in English, but with Dutch subtitles. So kids grow up essentially in a semi-immersion program of English as a second language, which gets reinforced later in life due to tourism and English being the current effectively most common language.
Stockholm is similar -- most people speak good English.
Amsterdam is one of the biggest tourist destinations in Europe, no wonder about the quality of their English (although this applies to the whole of Netherlands, not just Amsterdam).
I hear the Danes speak excellent English too, but I haven't been to Denmark myself.