How is the United States affected by its declining dollar? Is this a «bad» thing for the world´s largest economy? Actually, the dollar´s steady recent decline should be overall quite beneficial for the United States, which would explain the «benign neglect» of policymakers toward the currency´s slide.

How does a currency depreciation affect an economy? Normally, the most important effects are
1) an increase in exports, which raises AD and therefore GDP;
2) an increase in inflation, since imports become more expensive and their higher prices feed through into the CPI and also into production costs, pushing AS to the left;
3) an increase in the cost of debt, when it is denominated in foreign currencies. This aggravates the deficit and further increases debt, in a vicious rising cycle.
If we look at these three factors, we see that the unique situation of the U.S. economy leaves it benefited by the positive factor (1) and relatively unaffected by the potentially negative factors (2 and 3).
1) Thanks to the depreciation, U.S. exports are finally being boosted after years of dollar overvaluation against developing-world currencies, and the current-account deficit is declining. This is excellent news, both for the future of the dollar and for US GDP growth, at a time when many factors (subprime crisis, housing market) are causing it to slow down.
2) The weaker dollar has almost no effect on US inflation. This is because imports represent a very small part of the US economy, since the United States is quite self-sufficient in basic resources and is such a large economy. So higher import prices have little impact on the CPI.
But even those goods that could cause inflation in the United States do not rise in price like they would elsewhere, due to the unique U.S. status. Oil, a large U.S. import item, is sold everywhere in dollars, so the depreciation has no effect on its imported price for the United States. And other goods face the intense competitive pressure of the U.S. economy, so exporters or importers will accept profit reductions before raising their prices, for fear of losing market share. So the weaker dollar will have very little impact on U.S. inflation.
3) Like other developed economies, the United States owes all of its national debt in dollars. So the depreciation has no effect on its indebtedness.
What about other countries? Clearly, countries with large external debts denominated in dollars are helped by the decline and should see their debt-to-GDP ratios fall. Countries that exported heavily to the United States may see their growth affected as their products become less competitive. China is not one of those, since it continues to defend its undervalued currency against the dollar.
And what about countries with huge reserves of U.S. dollars and dollar-denominated assets? Well, they are clearly losing, in a big way. In fact, China is probably the last country that wants to see a dollar meltdown, because 1) it would lose an important source of export-led growth if it finally allows the yuan to rise and 2) its massive reserve assets lose value. So any «threat» by China to move its reserves into other currencies is no threat to the United States! Rather, it´s a threat for China itself, because it would produce further falls in the dollar and more losses for the Asian giant.
So should the United States be worried that countries are shifting out of the dollar for their foreign investments? Until recently, the world held 70% of its reserves in dollars. The United States is about 30% of the world economy, which should mean that dollar reserves would be closer to that proportion of the global total. Any changes in this proportion are natural and desirable. The euro is a new and important currency that should move into a larger role in world reserves and in the global economy. The adjustment now occurring has been inevitable for a long time. It will bring more balance to the gloibal economy, and will have little effect on the United States.
So what´s the drawback for the U.S. of a weak dollar? The main problem could be that it would be more difficult and more expensive for the United States to acquire new debt. But since the underlying problem of the U.S. current account deficit is not uncompetitiveness but overconsumption, anything that slows down debt acquisition is a good thing for the United States in the long run.
To summarize: the United States is not worried about the fall of the dollar, for good reasons. Other countries have more reasons to be concerned. The American who´s hurt the most is the tourist, who finds Europe intolerably expensive. But U.S. tourists can always go to Hawaii…