Steven Den Beste has a fantastic post on what it means to be American.
I've had the great privilege, recently, of spending some time with a man born in the USSR, who was employed in a very sensitive position in their government, and who is alive and here in the US today because of the courage of a State Department official. One of the things that he told me is that it is hard to be a Russian and not in Russia - there's too great of a tie to the land. I told him that it is a good thing that he is American, then.
After that, we drank a lot.
The point is, though, that being American is not about where you were born, or to whom you were born, but what you do and who you are. I grew up largely overseas, and most people both in the US and overseas don't seem to understand this. Americans don't understand that other places aren't that way, and non-Americans frequently don't understand that fundamental quality of Americans. Incidentally, this is one reason why I favor immigration and assimilation: it keeps the American spirit fresh and alive, because it provides a constant infusion of examples of the difference between America and everywhere else.