US $ are accepted in many countries. Often visa fees in SE Asia are quoted in US Dollars (USD) – they may or may not accept other currencies. In some countries the USD is the regular currency or the main currency anyway.
For example, in Cambodia the USD is used for almost everything but for change under US$1 local Riels are used. For the US this can actually be a nice benefit. US currency serves as a loan to the US government. When the USA prints dollars and distributes they avoid issuing bonds or treasury bills for their spending.
When interest rates were 10% on long term bonds if the USA had an extra $800 billion in currency floating around outside the USA they saved $80 billion every year in interest payments (when interest rates were 5% they would have saved $40 billion a year). In addition if those bills are destroyed or lost that open the way for the USA to put new USD into circulation and avoid that much borrowing.
It really doesn’t amount to a huge amount of help given how much the USA government spends but still it is a benefit. But with negative interest rates the reverse would be true. Currency offers what is normally seen as only 0% but in the crazy new world created by the central bankers bailing out the too-big-too-fail banks all over the world (creating massive amounts of liquidity [cash]) they started a path that has now led to the crazy situation of negative interest rates.
A negative interest rate means that say the German government borrows $10 billion today and pays back less money in 5 years. So if they got $10.5 billion today they would only have to pay back $10 billion in 5 years. This seems crazy mainly because it is.
Now the USA rates are not negative yet for long term rates (I think maybe in some really short term bills – under 60 days – it may have been). But negative interest rates have spring up in Euro denominated bonds from Germany (and a few other countries).
I find it funny that in such a case the USA would actually be giving those using their currency around the world a higher yield than those holding their long term bonds.
According the US Federal Reserve there is about $1.2 trillion dollars of USA currency in circulation (July 2013). The Federal Reserve estimates that the majority of the cash in circulation today is outside the United States.
The increased demand for the USD abroad also helps keep the USD value from declining in the face of huge trade deficits. To some extent we ship dollar bills to countries and they ship us food, cars, smart phones, etc..
Countries that use the USD as an official currency (though they may also have a local currency at least for small amounts – often under US$1): Panama, Ecuador, El Salvador, Zimbabwe and East Timor.
In some places it may seem on the ground that the USD is the official currency but it is really just the currency used without an official declaration: Cambodia, Peru and Uruguay