From my time abroad in Norway and other places, I have come to dislike Americans who pretend they are Canadian. That is probably one of my biggest pet peeves.
I pride myself in the fact that I have been told numerous times by non-Americans that I "do not seem like an American" and break stereotypes of what people think is a typical American. I mean, why travel abroad, pretend to not be American and just reinforce the stereotypes? I say be yourself and show the rest of the world that Americans are more than the stereotype.
The reality of it, though, is that there are plenty of Americans who do fit the stereotypes. However, if you are traveling abroad, you already break stereotypes--so go with it, and maybe you'll find it's better just to be yourself.
While we are on the subject of pet peeves; I have one more: native English speakers who use excuses as to why they can't or don't learn other languages later in life.
Let's face it, a good majority of the non-native English speaking world learns at least two languages growing up--with one of them usually being English. As many studies have shown, this makes it easier to learn more languages later in life. BUT, just because you grow up learning only one language does not mean it's impossible to learn another later in life. It may take a little longer, but everyone can learn a language. If I can learn one, as a math person, anyone can learn one. Stop wasting energy complaining and making excuses for why you can't learn another language, and focus that energy on actually learning one.