One of the few anime exceptions with an English opening would be Serial Experiments Lain with “Duvet.” The song is sung by Boa, a British indie rock band from London, and it was a recurring competitor in Anime Instrumentality’s Anime Music Tourney, in case you haven’t heard of it.
Now I haven’t seen the anime, but even so, you could tell the opening generally reflects the nature of the series itself. I really should hurry up and watch this series. From what I hear, Serial Experiments Lain can be quite the mind numbing experience. Although a lot of people sheer away from Lain because of its complexity, apparently. Which is a shame, because if nothing else, they miss the opportunity to watch this opening . . . To which I make this post.