The Dollar is a Global Currency:
After World War II, the world's developed countries created a plan in Bretton Woods, New Hampshire, to fix the rate of exchange for all foreign currencies to the U.S. dollar. Called the Bretton Woods agreement, the dollar was backed by its value in gold. By the early 1970's, to curb inflation, countries began demanding gold for their dollars. Rather than allow Fort Knox to be depleted of all gold reserves, President Nixon untied the dollar to gold. However, by that time, the dollar had become the world's dominant reserve currency. (Source: Chicago Fed, Strong Dollar, Weak Dollar)
The Dollar Is the New Gold Standard:
In essence the dollar is like the gold standard. Most global contracts, especially those for oil, are denominated in dollars. Many large economies, such as China, Hong Kong, Malaysia and Singapore, peg their currency to the dollar. When the dollar weakens, so do the profits of their exporters. These countries also hold large deposits of U.S. Treasuries, and could conceivably sell their holdings and cause a dollar collapse. However, it is not in their best interest.
The Dollar Has Always Recovered from Prior Declines:
The dollar declined during the 1970s, the early 80s and in 1991-1993. During these declines, there were also forecasts of a dollar collapse. Many countries discussed removing their currencies' pegs to the dollar. However, there was no real substitute as a global currency, so a dollar collapse did not happen.
Could the Euro Replace the Dollar as a Global Currency?:
In 2007, former Federal Reserve Chairman Alan Greenspan argued that the euro could replace the dollar as a global currency. At the end of 2006, 25% of all currency reserves held by central banks were held in euros, compared to 66% for the dollar. Furthermore, 39% of cross-border transactions were being done in euros, compared to 43% for the dollar. In many areas of the world, the euro is replacing the dollar. Furthermore, the EU has now become the world's largest economy. (Source: IHT.com, Greenspan Says Euro Could Replace Dollar, November 17, 2007)
However, even if the euro is destined to replace the dollar, it will happen slowly, and not cause a dollar collapse. That's because it's in no one's best interest for the dollar to collapse since it would completely destroy the global economy. Furthermore, the U.S. is the world's best customer. Therefore, the very countries that could cause a dollar collapse are those who need us to keep buying their products. Therefore, they have no incentive.
Another reason why the shift to the euro, if it occurs, would happen slowly is because of the eurozone crisis. The EU now sees it must become a fiscal and governmental union if it wants to continue its monetary union. Germany's Chancellor Angela Merkel wants this to occur, but the other members are very wary, as World War II are a too-recent memory. The EU's progress toward this monumental undertaking will determine the future strength of the euro in comparison to the dollar.