Decades don't usually have the courtesy to begin and end on the right year. The social and cultural revolution that Western countries think of when they talk of the " '60s" only got under way in 1962-63, and didn't end until the Middle East war and oil embargo of 1973-74.
But this one has been quite neat: the "Noughties" began with the Islamist terrorist attacks on the United States in 2001, and they ended with a global financial meltdown in the past year.
The Noughties is just a recent journalistic invention to make it easier to write end-of-the-decade articles like this. The term was launched several times in the last 10 years, but it never took off. Just as well, really, because it sounds a bit frivolous — whereas this was actually a decade when the tectonic plates moved into a new pattern.