This statue is apparently really scary. It doesn't just terrify Nebuchadnezzar when he sees it. Its image lingers, prolonging his freak-out, giving him insomnia, and imperiling the lives of all the Babylonian wise men in the process. Daniel, instructed by God, is able to narrate the dream and interpret it, but there still are some gaps in his interpretation.
Since Daniel was written (or partially written) while the Jews were being persecuted by Greek conquerors, it seems likely that the four empires Daniel describes were the Babylonian (as he says), the Median (which wasn't, um, really much of a thing), the Persian, as well as the Greek Empire of Alexander the Great and the divided Greek Empire that existed under Alex's generals (which is why the statue's feet are part iron and part clay—the empire's been divided).
The order of the statue—being made of gold, silver, bronze, iron (and iron/clay)—is actually pretty similar to the way the Greek writer Hesiod divides up the stages of human history. There's an initial, almost perfect Golden Age, followed by a Silver Age, a Bronze Age, and finally a really lousy Iron Age. (In Hinduism, they divide up the ages this way too, except you substitute Copper for Bronze.)
The Fifth Monarchy
But of course, there are always a dozen ways to skin a cat (if you happen to be some sort of psychopath in the cat-skinning business, we guess). People have interpreted the statue in other ways, too. For instance, Christian interpreters have often seen the Four Empires or "Four Monarchies" (as they were known) as being comprised of the Babylonian, Persian, Greek, and Roman Empires, followed by the rise of Christendom—the mountain that fills up the world. If you want to look at the statue that way, you could probably see the final divided Empire as being Rome, which was later divided between its Western and Eastern halves.
In fact, this little nightmare (or prophetic dream) has inspired a lot of speculation throughout the course of history. Daniel ranks next to Revelation as source material for people who are speculating on the end of the world. For instance, in Great Britain during the seventeenth century (after a civil war had temporarily overthrown the monarchy and killed the king), there was a group of religious revolutionaries known as the "Fifth Monarchists." They believed that the Second Coming of Christ was at hand and that Christ would establish a "Fifth Monarchy," like the rock that fills up the world in the statue dream, erasing all previous empires. (source)
Also, if you think about it there also might be an echo of the David and Goliath story hidden in here. David kills the giant Philistine with a small stone throne from his sling, just as the rock representing the Messiah destroys the statue of Empires. And the Messiah who will destroy this gargantuan Empire Statue is supposed to come from the house of David (as both Jews and Christians tend to believe).