The U.S. dollar is a "fiat" currency, and it is therefore not backed by any tangible commodity, but rather the "full faith and credit of the United States," as is printed on every Federal Reserve note. According to the Federal Reserve, paper currency has not been redeemable for gold or silver since January 30, 1934.
Every major currency in the world today is fiat currency. The final break between the U.S. dollar and the value of gold came in 1971, when the U.S. abandoned the gold standard once and for all. Today, according to HowStuffWorks, the only reason the dollar has any value at all is that it is issued within the context of a society full of people who have agreed to treat it as though it has value. Without that faith, every major currency on Earth would be as useful as small pieces of paper generally are. In a sense, therefore, the dollar, as well as the euro, yen, and every other major currency, is backed directly by the stability of the society that issues it, rather than by a metal that can fluctuate in value from one day to the next. This means that the bills in a wallet have value because, as economist Milton Friedman put it, "Everybody thinks they have value."