Of course, if us rest-of-the-worlders did get to vote, we'd vote pretty solidly Democratic. According to this article in the Washington Post, most of the world prefers Barack Obama to Mitt Romney, and it's not even close.
So why do non-USians have such a high preference for Obama, far greater than Americans themselves? A few reasons.
It's fair to say that a lot of the disillusionment within the US towards their President is due to the economy, and those of us outside the country aren't particularly affected by that.
Obama is also following on from George W Bush, who started two unpopular wars which many other countries are embroiled in, and is widely regarded as a buffoonish sort of character. It's not a hard act to follow. But Obama is the anti-Bush, and the antithesis of the stereotypical ignorant American. He has lived abroad, has a clear fluency with other cultures, and is obviously intelligent and thoughtful.
There is a perception that Americans view the rest of us as somehow beneath them, since the US is obviously the pinnacle in human civilization in some Americans' minds. Bush's behaviour in office certainly gave credence to this perception, but Obama has managed to garner back some of that lost goodwill.
But what is most interesting to me from the Washingon Post article is the comments section, because I'm fascinated by the views of the masses. Now I certainly do not think that what a few people say in the comments sections of newspapers represent the entirety of that country's opinion, by any means. But they can tell you a lot.
That last one makes a fair point about Israel not being listed, but then is possibly implying that Obama's watery liberalism is akin to Hitler's National Socialism.)