I agree, a single government would be a good thing, as long as it's a democracy and not a totalitarian regime, but I don't think such a thing could actually exist, maybe in the future but not at the moment. A single government would mean a single state which would technically be an empire and history has shown they haven't lasted for very long.
I suppose you could argue that we're on that path now with NATO, the EU and the UN; perhaps these will gradually evolve into a world government. All three organisations currently have a lot of power and are responsible for many laws in member states which I think will continue to increase. Take the EU for example, they're trying to push a single constitution that will affect all member states but they've so far failed as most people don't want a United States of Europe.
We've already been close to having a nuclear holocaust in WW2 and the cold war and a single government could've ruled the world if the aforementioned conflicts went the wrong way.