"Citizens by birth or choice of a common country, that country has a right to concentrate your affections. The name of American, which belongs to you, in your national capacity, must always exalt the just pride of Patriotism, more than any appellation derived from local discriminations." --George Washington

"There is no room in this country for hyphenated Americanism. When I refer to hyphenated Americans, I do not refer to naturalized Americans. Some of the very best Americans I have ever known were naturalized Americans, Americans born abroad.

“But a hyphenated American is not an American at all. This is just as true of the man who puts “native” before the hyphen as of the man who puts German or Irish or English or French before the hyphen. Americanism is a matter of the spirit and of the soul.

“Our allegiance must be purely to the United States. We must unsparingly condemn any man who holds any other allegiance. But if he is heartily and singly loyal to this Republic, then no matter where he was born, he is just as good an American as any one else.

“The one absolutely certain way of bringing this nation to ruin, of preventing all possibility of its continuing to be a nation at all, would be to permit it to become a tangle of squabbling nationalities, an intricate knot of German-Americans, Irish-Americans, English-Americans, French-Americans, Scandinavian-Americans or Italian-Americans, each preserving its separate nationality, each at heart feeling more sympathy with Europeans of that nationality, than with the other citizens of the American Republic.

“…The man who calls himself an American citizen and who yet shows by his actions that he is primarily the citizen of a foreign land, plays a thoroughly mischievous part in the life of our body politic. He has no place here; and the sooner he returns to the land to which he feels his real heart-allegiance, the better it will be for every good American.

“… For an American citizen to vote as a German-American, an Irish-American, or an English-American, is to be a traitor to American institutions; and those hyphenated Americans who terrorize American politicians by threats of the foreign vote are engaged in treason to the American Republic. " –Theodore Roosevelt, 1915

So, too, would I include those would refer to themselves as: African-American, Hispanic-American, Arab-American, Asian-American, et al. We are one people of many ethnicities, but one unique culture: American. If you feel you cannot refer to yourself as such without hyphenation, then do as Roosevelt suggested and leave. (Thanks to Rick for the link.)