Wouldn't you rather celebrate the changing seasons? That's a tropical year (named from the Greek tropi which means "turn," from whence the Tropic of Cancer and Tropic of Capricorn derive; not for tropical climates*, where, as we know, the seasons are not so marked). It makes the most sense if you're basing your calendar on the changing seasons. The equinoxes and solstices would continue to line up on the same dates over time (the new year would fall on the winter solstice, for instance).
But perhaps you want to align your calendar with the motion of the Earth through space. But relative to what? Relative to its perihelion (closest approach to the Sun)? That's an anomalistic year. Relative to some distant stars? That's a sidereal year. Want to count up from the number of days that it takes to get the Sun back in the same position? That's a solar year. Perhaps we could use the motion of the Moon to define a year - but we know that won't work out to be the same as the others, either.
The truth is, none of these years are precisely the same, and there are good reasons for that (basically, the motion of the Earth through space is not as straightforward as one would hope). So we have to pick a standard and go with it. And picking that standard is... well... like I said, arbitrary.
So we picked the Julian calendar as our standard (365.25 days per year) and thus we celebrate the New Year on January 1st. It's not what other civilizations have chosen, but it works. I, for one, am torn - as a scientist, I'd love to use sidereal years, to base my calendar on the broadest and most thorough scope; but as a human being, as a gardener, as someone who loves to watch the seasons change, I'd prefer the tropical year.
Ultimately, it makes no difference. Regardless of what calendar we choose, we will have regular holidays (Christmas is always December 25th, for instance) and floating ones (the date of Thanksgiving varies year to year). We'll still have to add complications to our chosen system to account for time zones and axis precession and so forth. We'll still have people who disagree and use a different system (heck, we can't even decide whether to write the date month-day-year or day-month-year). But I think it's only fair that we admit it: January 1st has no meaning unless we grant it meaning. Our choice of this particular day is arbitrary. It's not even a "nice" choice that simplifies calendars or coincides with something obvious. It just is.
Happy New Year, everyone.
*Instead of double-nesting parentheses, I'll add here: "tropical" places are those which fall in between the two Tropics on the globe, and it is only incidental to the etymology that the weather in the "tropics" seems so standard. In fact, the weather in the tropics isn't standard, anyway. What we think of as standard tropical weather is actually standard tropical maritime weather. The temperature of the ocean likely has more to do with the climate in places like the Caribbean and Hawaii than does the latitude.