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Interesting question! But obviously it's not as easy (nor very likely).Actually, you can say that at one point, Gold was the single currency of the world. But if you are talking about paper currency (like Euro)
(i) who will print it? (If a "central world bank" does it), how will it be distributed? Countries would NEVER agree on its distribution mechanism. (Even the Euro has a lot of problems but since the number of countries that use it are not that many AND they are developed with a robust an credible statistical institution, it seems to be working for thm
(ii) In case of problems, who will decide/be the judge?(iii) If it does get implemented, a LOT of things would get simpler (trade e.g.) and the world interest rate would most likely become the same!
Such a shift might end up doing more harm than good. It would mean that if the currency was hit by a negative shock, then no country would be spared of the fallout. It would also limit the flexibility of policy-making, such as those concerning exports and imports. Moreover, we have already seen in the experience of the Euro region that integration can be a complicated affair, even when the countries are at a fairly similar level in terms of development. Attempts to unite the most developed economies with the least developed ones is therefore unadvisable.
