Dollar would be worth less relative to other world currencies. Thus, demand for U.S. goods in the international market would increase, and demand for foreign goods in the U.S. would decrease. Thereby, benefiting the balance of payments and improving the U.S. trade imbalance. In wake of losing comparative advantage with the U.S. in terms of exchange rate, other countries can protect their local firms through protectionist policies, higher tariffs, and duties etc. This would make U.S. goods expensive for foreign consumers and equate the depreciating dollar advantage of the U.S.
Furthermore, the U.S. economy can benefit a lot if depreciation in dollar helps to increase exports and decrease imports. An increase in exports could stimulate demands and push firms to hire more people. This would be a good sign for the U.S. economy which is facing an unemployment rate of around 10%. Furthermore, the U.S. companies would get more revenue from selling abroad, and thus, would be obliged to pay more taxes to the government.
However, a depreciated dollar can have negative consequences both for itself and the world. Oil is traded in U.S. Dollars on the international market, and oil and dollar share an indirect relationship. That is; a rise in dollar value decreases the price of oil, whereas a fall in the U.S. Dollar increases the price of oil.