On who's what: Like many people of Eastern European ancestry (Jewish, Slavic, Baltic, German...), I have some Asian ancestry which doesn't show up in genealogical records. Doesn't show on me, either; does with my maternal grandfather's family.
Hispanics: I've met Mexican-Americans with not just varying admixtures of European and American Indian ancestry, but one who's put Chinese and one who was part Eskimo.
There are people born in Buenos Aires, whose ancestors go back several generations in Argentina, who consider themselves Italian.
Where I grew up, one of the local heroes was Tom Quick the Indian killer. Indians killed his family; he vowed to kill a hundred Indians in revenge. (The story is that he got up to 99, and on his deathbed pleaded for someone to bring him one more Indian.)
About ten years ago, I realized that all of Tom Quick's descendants I'd known were also part Indian.