I definitely don't wear an American flag or anything signifying I am American when I travel. I don't own anything overtly "patriotic" (that word has been stolen somehow). I even have some Canadian t shirts and sweatshirts. But I do introduce myself as American when traveling.
My best joke when I travel to Canada: "First off I would like to apologize for the political state of affairs in my country. I know we make y'all (this is important to add...Canadians like southern accents) feel like you live in a wonderful apartment perched right above a meth lab".