The dollar just happens to be the international currency of choice. Preferred by terrorists, North Koreans, and a host of countries world wide for regular business, backed in full by the economic powerhouse called the USA. Perhaps one day the Euro will make it up there, but not too likely in the near future.
You have to realize that exchange rates float, and are not really backed by governments. And the US government really has no incentive to strengthen the US Dollar. Our economy is bursting at the seams, our national debt (which basically is the psychological driving force that weakens the dollar) though numerically high, is only a tiny percentage of our gross domestic product, we are at more than full employment, so we have plenty of cash sloshing around in our coffers and plenty of cheap, fun things to buy with that cash. That being said, it literally "pays" for us to be importing everything and anything which costs less to produce overseas (ie, countries with a "weak" currency). We can dump paper currency, and get real stuff in return, like toyotas, and Chinese made furniture, etc. Boeing I would guess is our biggest exporter of heavy equipment, and there is no shortage of demand for their products. Our farmers produce a hell of a lot of corn and wheat for export (or conversion into alcohol should we chose to do so). This keeps our workers employed, we pay them in dollars, and get some of those exported dollars back when we sell planes or grain. Because our economy is strong, and inflation low, productivity is high for what we do produce, those dollars go right back into circulation, improving the economic outlook of the local sellers. Now reverse the situation, and look at Europe and EADSs. Their Euro is "stronger" than our dollar. If I travel to Europe and want to eat, I get creamed. A hamburger I can get for lunch here costs $4, the same meal in London runs $10-15. So I don't go. On a larger scale, France is building a big airplane, that is delayed and delayed again, and with each passing month costs more to buy, (but not necessarily to build), because the contracts were in the international currency: the dollar. Who wants to buy a $500million aircraft (exaggeration, sorry) with limited functionality, when you can buy 2 787s for $250million, or half the price? Obviously I'm simplifying, but there is a reason that Airbus sales are going down, and Boeing can't keep up with the demand. This is very bad economic news for them, and it is not limited to aircraft. Having a "strong" currency may boost national ego, but it is not necessarily a good thing in the short run.
"Trust, but verify!" An old Russian proverb, quoted often by a modern American hero