It's a remarkable thing, this celebration of the New Year. It's not like things are suddenly far better or far worse just because the calendar ticks over and we add one to the year. It's more of a functional thing these days, as the record-keeping and data-crunching changes one of the four digits in the year and we keep going one day at a time.
The recognition of a New Year, however, despite Dick Clark's longevity to the contrary, is not at all a new thing. Ancient people recognized a new year. The Babylonians, who knew a thing or two about astronomy, marked the first New Moon after the Vernal Equinox. This was not long into spring, which was a time of renewal of crops and planting and all manner of other survival-minded things.
The Romans, not wanting to seem inferior, followed in those footsteps, so much so that they marked the new year in spring as well — which, by our way of thinking, is nowhere near January 1. (I challenge you to find a part of the planet that has its January 1 in the middle of spring.)
But the Romans, ever wanting to improve, began to play around with the calendar, with this and that emperor moving things along ever so slightly, in the middle of naming buildings and statuary after themselves. Soon, it was all out of whack.
Leave it to Julius Caesar to fix things. (He fixed a lot of other things as well, among them the whole of Roman law and the border with Gaul &151; after he got through with the Gauls, they didn't need a border anymore.)
Caesar declared that January 1 was the start of the new year. This was just fine, if you look at things in a certain way, as Caesar often did, because January celebrated Janus, the god of beginnings. So the first day of January began the new year. (Caesar's moving the beginning of the new year meant that one year had 445 days in it, but that's beside the point.)
With the passing of the Roman Empire came the Dark Ages, and the ignoring of the celebration of New Year, for a few hundred years, at least. But things got back on track in the Middle Ages, and we've been celebrating the beginning of each new year ever since — even if it's in the middle of winter (or summer, in the Southern Hemisphere). One exception to this, of course, would be the British Empire, which took until 1751, when the Empire was beginning to be on its way out, that the beginning of the year shifted from March 1 to the more commonly used January 1.
Other cultures, mainly Eastern, still celebrate the New Year on other days. Western tradition, however, has the vast majority of New Year's celebrations on the first day of January. Caesar would be proud.