People have been predicting all sorts of calamities since the 1980s-that's how they sell books. But as several have noted, the dollar's sharp drop since 2001 ( I think it was actually 88 cents to the Euro in laste 2000) is, if not a collape, still a big move and a big deal.
The reasons are complex and I'm no expert. But much of it has to do with the markets' perception of each country's relative economic strength and short to mid-term outlook. The US dollar has been hurt by huge budget deficits, which show no sign of turning into surpluses quickly due to, primarily, the war in Irag. Putting politics and what you think of the war aside, the huge costs are funds that other countries spend on quality of life. Rant all you want about the socialistic societies of the "old Europe", but they have much broader medical, educational and retirement benefits, and much lower relative budget deficits. Hence stronger currencies. How do they do it? Well, they basically have let the US bear all the costs, financial and otherwise, of defense since the collapse of communism. Getting everyone back to the table and bringing their checkbook with them should be a big priority for the next US administration.
The most recent drop in the dollar is caused, IMO, by the world's perception that the US will have to lower interest rates to stimulate the economy and dampen the effect of the housing bubble deflating, which we've begun to do via the Fed rate drop on Tuesday. If a country has room to keep rates relatively high, it results in a stronger currency, and vice-versa. Today, we're the versa.
One crushing economic factor is oil. Look at the percentage of energy the US produces itself compared to what it uses. That's the true big change since the 1980s-we now produce far less ourselves, thus sending more of our money overseas-our wealth declines, their wealth increases, dollar goes down. It's as simple as the motel with a better vew charging higher rates and making more money. And while we are more focused on saving energy, there is still a real disconnect for many people. If you don't believe me, take a long look at the size of the vehicles you see on your way to and from work.