It has been suggested that the world could be governed in roughly the same manner as the EU, eg, via the G20 mechanism. But ruling the world is a rather manic occupation. It seems like many think technology is going to make governing the world possible and "trivial" things as cultural differences are forgotten.
What is causing this mania is a depression stemming from the Great Recession where the West has entered a dark mood and emerging nations are becoming rivals, not partners.
If I have understood this correctly, the reason for why the Euro is in danger is that there is no political frame for the currency region. There does not seem to be enough political will to govern the EU and to talk about governing economically but not politically seems desperate not knowing how. Therefore ruling the world would be more difficult and should not even be discussed. Rather should diplomacy as delineated by the Obama administration be promoted. Networking rather than hegemony because fragmentation forces are greater than the opposite.
Personally I think sticking to our values of liberty, the rule of law, democracy and spirituality thus maintaining the most livable condition is the key to continued success.