The dollar operates on supply and demand just like all (ok, most) other goods. Think of a “strong dollar” as meaning “a high-priced dollar”. Goods’ prices rise when there is one of two things — high demand for them or low supply.
So you can think of it as two-fold… as american companies feel the sting of the economic downturn, they lower prices. This causes foreigners to demand dollars in order to buy our stuff, thus putting upward pressure on the value of the dollar. Second, there are fewer dollars in supply because the companies who have all the dollars are not lending them to anyone. this also puts upward pressure on the value of the dollar.
Please do not accept this explanation as 100% true… the forces that control international monetary exchange rates are numerous and complex. But for a simple explanation, this ought to do.

Most of the world is in a recession right now. What was once one of the two or three richest countries in the world on a per capita basis (Iceland) had it’s currency lose half it’s value in a few months. That’s a Latin America or an African style currency crash in a wealthy European nation. That hasn’t happened in decades.
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Despite some bad publicity in the last decade, the dollar is still the pre-eminent world currency. And it is the most liquid currency in the world. The euro still does not engender that much faith in a time of absolute crisis.

In addition to Hello G’s valid points, you should also realize that the value of a dollar is in comparison to currency of other countries. Most of the world is in a recession (probably caused by the US recession, but that’s another topic). So, if every country is doing equally poorly (a false assumption to make a point), the dollar will be just as strong as it is in good times.
The US is a major market for goods produced in other countries. When Americans are in a recession and not buying as much, those countries can’t sell as much. Which gets you back to G’s point that the people with dollars are keeping them, making the demand go up.

It is called flight-to-quality. In bad times people want just be sure that their money are safe, and just about the most safe thing is dollars and especially US treasuries, because USA is the world’s largest economy and the world’s reserve currency. Equally you see that in a global recession, that the smaller country, the more will the currency fall, unless the currency is pegged to some other currency.

Because the rest of the world is worse off than America is. I’m guessing you think America is worse off than the rest of the world because you have been hearing Bush hating liberals make up lies for the last 8 years trying to blame every bad thing in the world on Bush and screaming that things in America were a lot worse than they really were.

our economy is in better shape then the majority of the worlds economy as of right now.

it not JUST A ONE DAY UP TICK