Damn, this is a frog-in-the-well set of answers we have here so far. Think GLOBAL people. This London vs. New York debate that is going on in the other answers is a joke.

This is not like competing to host the next Olympics. Hosting the capital of the world is the opposite of the expression of national pride. It is an expression of national weakness and insignificance, gracefully turned into a strength.

The correct answer is Dubai.

The explanation is a complex one, but roughly similar to why Brussels was the right choice for the EU.

Let's zero in on Dubai via elimination, before looking at the positive attributes that recommend it.

You don't want an old city with a lot of history and baggage associated with a single powerful nation state. ESPECIALLY not an old city from an old and powerful country. You want a new city with very little baggage and lots of future, preferably in a country with no power.

Brussels isn't quite that for Europe, but Dubai is a better Brussels for the world than Brussels is for Europe, if you follow my logic here.

Singapore is a close #2, but it's a little too important in real terms to serve, for the same reason NYC is too important to be the capital of the US.

Why Dubai? Let the eliminations begin.

1. Europe, Japan and Korea are breeding themselves into extinction. Out. Too damn ethnocentric and culturally self-superior as well.
2. North America is out because we are entering the "Post-American" world as Fareed Zakaria calls it, defined by the "rise of the rest." And America has never really had anything even crudely resembling a globalized sensibility. During the American age, others simply put on American appearances to get along with the big guy. Oh yeah, Canada is in North America too. Well... moving on.
3. South America is out. They party too much. Too bloody happy.
4. Australia? As the famous "end of the world" video (http://www.youtube.com/watch?v=n... ) noted, f***** kangaroos.
5. Africa is out. No place is stable enough with a decent institutional base. Plus you don't want to combine the world's bureaucratic heart with its spam-email soul into one explosive black hole.
6. Old Asia is out. Both China and India are far too insular and self-absorbed, and far too anxious and thin-skinned about their emerging role in the world.
7. Asian Russia and Mongolia are out too. Nobody wants to go there. You want a place pigs-at-the-trough bureaucrats will be happy and distracted between dull negotiations about trade caps and standardized sausages (I am stealing shamelessly from Yes, Prime Minister logic here).
8. Oceania has a peculiar appeal: places like Tahiti or Easter Island. But you can carry a joke too far. I like those Easter Island statues though. They look like proper bureaucrats.
9. Seriously though, this really leaves two critical regions that will drive the next 100 years: SE Asia and the Middle East.
10. On the face of it, there is no contest: SE Asia is the hot economic zone for interesting growth. The Middle East is in sunset mode along with oil, while SE Asia is on the ascendant. The Straits of Malacca are rapidly becoming the fulcrum of the world. 70% of the world's shipping passes through there. The region doesn't have vast hinterlands like China or India, so the countries of the region have a more global sensibility. Europe is represented through even presence of Dutch, French and British colonial hangovers. America is represented via a memory of a bad headache lingering over from Vietnam. India and China are represented in lower level cultural layers.
11. But on the other hand, the Middle East is inventing a new post-oil future for itself. If you've been to both regions, you also know that Dubai is more cosmopolitan than anyplace in SE Asia. Yes, there's a local culture there, but it isn't a big, overhanging presence. As oil reserves go down, the place can only become more open, not less, in order to survive. And we've got to give them something to do. Paperwork seems like a good idea, especially since they've shown a remarkable inclination (nothing to do with Islam, this goes back to long before Islam) to start bloody wars when they don't have enough to do. Remember, bureaucracy was invented just across the gulf in Iraq (it was called the Code of Hammurabi, and documented carbon emissions caps and some rules about disposal of toxic lead batteries).
12. For the sake of completeness, and to get this list to a round dozen point: Antarctica. No.

Now for the positive attributes. The precedent of Brussels helps.

Brussels was at the interface of the Catholic and Protestant spheres. It was a pawn in the game of Europe.

Today, it is great as an EU seat because it (frankly) is mostly insignificant in every other way. Fun country. Good beer. Tintin. The Mannequin Pis. Good fries. I've been there: the people are very nice. Bureaucracy and happy hour. Great competencies for a capital. Enough for pigs-at-the-trough bureaucrats to do during their off hours.

But overall, come on, nobody takes Belgium very seriously. That's why it is a great location for an EU capital. London and the French would have objected. Paris, and the British would have. Fill in the storyline for other major European capitals.

That's why Brussels worked well.

Dubai will work well for the same reasons, except even better. It DOESN'T have a long history. It's a clean slate. They've already developed quite a competency in bureaucracy (outsiders do all the actual work; the locals work in government). All they need is a competency in beer. Brussels and DC can consult.

What's more, the whole damn region is so messed up now, the only way to improve morale and resocialize the region into world society is to give it a bit of a promotion into the middle management in the hierarchy of the world.

Israel will sulk, but then, they always do.