If you mean the US variety, it is a global currency, by any yardstick. The US dollars account for somewhere around 50% of international financial transactions daily. Besides that, the dollar is also the world's prime reserve currency, since approximately two-thirds of the FX reserves across countries are dollars...
If not dollar, then what?
Yuan. Currently the dollar is the most relevant international currency for sure. But its status as reserve and trade currency is slowly but steadily degrading. China, Russia, Iran, South Africa and Brazil are working together to end the dollar regime. I think it will take years, maybe decades, but in the end the US will face tough times, because most of the US wealth stems from the strength of the dollar.
Of course, using Bitcoin instead of a national currency for global trade would be the most neutral and most efficient solution. But I think this will not happen in the near future. Bitcoin's emergence as a global currency will not be the result of an official decision. It will be the result of the power of the free market that strives for the best solution.
ya.ya.yo!