Keeping track of the right time has gotten easier. Atomic clocks sit aboard all 24 GPS satellites, and anyone with a GPS - or even a cell phone (most of which receive periodic atomic-clock-time updates) - has the right time to a tiny fraction of a second.
The falling ball at Times Square does not. That's normally off by a second or two. Don't trust it if you're a Type A person who wants to begin the year with precision.
Since 1972, we've kept our clocks officially synchronized with the actual turning of the planet. There's even an agency in France called the Earth Rotation Service that monitors our spin to make sure that the time ballet remains choreographed. Leap seconds are sometimes added, thanks to our system having being calibrated to the length of the day as it was in the mid-19th century rather than its value now; but none will be inserted in the final minute of 2009.
Step out after all the cheering and gaze at the sky, and you'll see the result of this excellent timekeeping. Each New Year's at midnight, the stars and constellations assume the same exact position as the year before. Sure enough, there's blue-white Sirius, the Dog Star: the night's brightest, coincidentally at its highest and due south exactly at midnight. Each year you'll see brilliant Capella nearly straight up, and Orion halfway up in the southwest.
This year, though, there's something special: For the first time since 1990, we have a New Year's Eve Full Moon. All Full Moons reach their highest point around midnight. But to continue with our theme of precision, consider that the time of perfect fullness came 9.75 hours earlier, which will place the Moon's moment of hovering highest-up and precisely due south at 12:24. Fine: just after midnight. Have some champagne, then venture out.
A New Year's Full Moon is always in Gemini, and it's always a blue moon - meaning that it's the second Full Moon in the same month. Now look to its lower left. This year there's a bright orange star there: Mars!
Thus you'll start the year as timekeeping civilizations always have: by gazing into the still-mysterious universe, whose nature is ultimately timeless.