I'm just Puerto Rican, though my great great grandmother(or was it father?) was black.
And yea, there comes a point where you can't claim your Nationality anymore as lazlo mensioned. Hes American, his Irish roots are so far removed claiming them would be stupid. I'm 1 generation removed from Puerto Rico, and my parents speak spanish and such, but I know my kids(with my limited spanish) are gunna be further removed from it, and their kids, well they wont be able to claim the nationality without being pozers.
But ethnicity is different from nationality, so if you've got europe in you, instead of listing every country, shorten it up and say "white".