To many people from other cultures I'm pretty sure that Americans do
appear to be rude. I'm sure it's not intentional
and usually just boils down to a mixture of brashness (which seems to be something quite worthy
in US culture) and possibly unintentional patronism.
I'll give you a couple of examples, from a British perspective. To most Londonders the stereotypical American tourist will be somewhat overweight, have appalling dress sense and most importantly, will be loud, oh so loud. Whereas in Britain it's considered mildly rude to talk loud enough for others to overhear your conversation, in America the general attitude seems to be that whoever is the loudest gets most noticed (and by implication gets what they want).
Now I know that not all Americans are like this: I've met plenty of them both over here and when I've been to the US that weren't completely overbearing, didn't weigh over 20 stone (although the number of seriously obese people I see when I'm the US is very frightening), and don't feel the need to shout all the time. But for obvious reasons if you take a city of 8 million people and put in two Americans, one who is being loud and obnoxious, and the other who is doing their best to blend in with "the natives" and it's pretty obvious which one will be most noticeable.
As to the patronising thing, one example will forever stick in my mind. A friend of mine used to work as a waiter at a West End restaurant to pay his way through college. The money was lousy but the tips were good (same old story), and once a month he used to go to the bank and change a couple of hundred US dollars into real money. When I asked him about this he said that a hell of a lot of American tourists would leave a $5 bill as a tip. What the hell? This is England ... we have our own currency! It's stronger than yours as well, 10 of our £ sterling buys more than 15 of your dollars. We're not some third world country desperate for hard currency. But even when my friend managed to run after whoever left him dollars as a tip and explained this, nine times out of ten he was met with a blank look or a quizzical expression.
And that is why many Brits consider Americans to be rude (as well as a little bit stupid). Of course it's a generalisation, you cannot speak about any nationality or race as a homogenous block. But unfortunately for the millions of intelligent, witty, thoughtful Americans out there, there's an awful lot of work required for you to rebuild your countrymen's reputation.