Continuing on with the "American" debate:
We derive "American" from our name: United States of America. Hence Americans. The only other term that would roll off the tongue easily while still evoking the culture of the USA would be what? Yankee? Unfortunately that term already has other meanings: To Europeans (from what I understand), it can mean a person from the USA, to a person from the south part of the USA (the old CSA), it can refer to a northerner, and to a northerner, it could refer to someone from the New York area (sometimes). You can see how that would be confusing to call everyone from the USA a Yankee.
Moving on, people generally derive what they call themselves from the name of their country, not the continent (with some exceptions like Australia which is both a country and continent name). Hence, people from France are French, people from Saudi Arabia are Saudi Arabian, people from Estados Unidos Mexicanos are called Mexicans, and people from the United States of America are Americans. It makes perfect sense really. I don't quite understand why anyone would assume that someone is referring to the continent of North America when they say "American". I mean, when people call themselves "American", or "Mexican", or "French", or anything, they're referring to their nationality. And since the USA is the ONLY country with "America" in it's name (as far as I know), when one says "American" to refer to nationality, there's only one country they can actually be talking about: the United States of America.
As a final question: Steephie: Are you from the US? Or from another country? I'm honestly curious since as far as my experience is concerned (from USA), when people in the US say "America", they are NOT referring to the continents of N. and S. America. Perhaps to people in "the old world", "America" means N. and S. America, but here in the "new world", when we want to say North America, we say North America. South America is South America. I have hardly ever heard anyone refer to the two continents as "America" outside of a world history course when they're talking about the age of exploration when Europeans first colonized the "new world".