Beautiful Goog doodle! This one is pretty clear; there's a dog in the logo because the year 2006 in China is the year of the Dog, as I said before. He also got a paper in his mouth with some chinese character on it. It's difficult to see what charachter it is as I'm not chinese myself, but it is either '狗', wich means 2006, or '戌', wich means dog. And finally, some fireworks at the right to celebrate the event.
Google is linking to these page results.
New year in China always falls on a different date, every year. As you now know, New Year 2006 was today, on the 29th of January. Next year, Chinese's New Year 2007 will fall on the 18th of February.
As Wikipedia explains:
The day of the second new moon after the day on which the winter solstice occurs, unless there is an intercalary eleventh or twelfth month in the lead-up to the New Year—in such a case, the New Year falls on the day of the third new moon after the solstice.
During the years at Google I have collected the previous Google doodles celebrating Lunar New Year:
2001
The year of the Snake
2002
I wonder why they haven't done it that year...
The year of the Horse
2003
The year of the Goat
2004
The year of the Monkey
2005
The year of the Rooster