A federal world government (Perhaps something like the United Federal States of Earth) seems like a fundamentally good idea. It would mean that international co-operation be a lot easier, the planets resources can be used and directed towards big projects like colonisation of the Moon or Mars. It also seriously reduces the chances of war, and any radical dissadent organisations can be easily crushed (Imagine the Taliban V The World. A unified world government would mean that resources can be more fairly distributed, energy can be shared, easier to hunt down criminals gone into hiding, international trade improves etc.
The fundamental problem is that this requires that nations sacrifice their own political sovereignty to that of the of federation. You only have to look at the unpopularity of the EU to see the problems of uniting countries together. Humans tend to put their nation first before their own species, rather than the other way round and will therefore resent foreigners having a say in their own affairs. The EU is essentially a microcosm of attempting to bring together nations into a union, anyone interested in the concept of a world government should look into the EU to find the sort of problems this causes.
Also, you have other problems like different cultures, most thorny is Islamic Culture, who, due to their religion and Sharia Law, would possibly make it impossible for them to integrate into a sort of world government. Really, it is probably better and easier to bring together nations that share common values and interests. Perhaps the EU, USA, Commonwealth Nation's like Canada and Australia, possibly India and South Africa, Japan and maybe Taiwan and S.Korea could unite.
