Even as a kid growing up in Denmark, with all the British/American shows on TV (not dubbed) it was easy to learn a lot just by reading subtitles and following along. I give Saturday morning cartoon re-runs a lot of credit for helping me to learn. I remember sitting on a train with a friend of mine and us both realizing that we both knew a lot of English a year before we were going to start learning it in school.
I've found that most Scandinavians (or at least Danes) have a pretty easy time with English. Because the sentence structures are so similar, you're mostly plugging in English words that you're already familiar with and using the same sentence.
That said, on a deeper level, English is a very different language. That's most likely because it is such a cross between other languages.