The second full moon
in a single month is a fairly rare occurence, rare enough that it's called a blue moon. A blue moon occurs every 2.7 years because our twelve month calendar doesn't quite match the lunar cycle or the time it takes for the moon to revolve around the Earth. A lunar cycle takes 29 days, 12 hours, and 44 minutes. Roughly. I should note that the moon doesn't, unfortunately, turn even slightly blue, but it's still an additional opportunity to view a full moon.
New Year's eve this year is a blue moon; we've already had one on December 2. But it's even more nifty than that. First, while a blue moon occurs about every 2 and a half years, we haven't had one on New Year's Eve since 1990.
For those of us in most of Europe, Africa, Asia or Australia, the New Year's blue moon will also partially eclipse; lucky viewers will see a noticeable darker edge along the moon's full disk.
So when you're making your resolutions, and drinking that sparkling wine, give a thought to going outside for a moment, and admiring our lovely satellite in all her glory. May 2010 be a year of peace, beauty, and abundance for all of us.