I think one of the biggest problems in our world is that all the governments are very obstinate when it comes to making international agreements. This issue could be well observed at the Copenhagen climate conference last year.
Therefore I suggest that we create a world government directly elected by all the people on earth. This government would be able to deal with all the unsolved global issues like climate change, world hunger or collapsing financial systems.
Well I have to admit, this isn't really my idea, I adopted it from Andreas Eschbach's book "Eine Billion Dollar" (German for "One Trillion Dollars") where a nobody inherits one trillion dollars and thinks a long time about what to do with it. It's a really good book, unfortunately only available in German, as far as I know...