I'm reminded of a quote by Billy Connolly. He said "Political Correctness is the language of cowards" and I couldn't agree with him more.
I take the already mentioned case of "African American" folks. What a stupid bloody term. If they don't wanna be called black, fine, but African American is just plain dumb. My ancestors come from: Ireland, England, Wales, and I think German. But that doesn't mean people have to refer to me as an "Irish Australian" or a "German Aussie".
I'm Australian. I live here, I will probably remain here for a very long time and I live like one. Likewise with many of the so-called African Americans in your country, I'll bet.
That politically correct term is far more rascist than referring to someone by the colour of their skin, because that's just a description, whereas the other suggests that "Well, I'm fine with you and all, I'm just not gunna class you as an American like me, because you're black, and like, different and stuff"
You see my point? Politically Correct people are doing more harm than good, IMHO.

Well, that's what I reckon, anyway...