Different cultures observe their New Years at different times of the year. Generally, the New Years dates are linked to seasons, solstices, or equinoxes.
The celebration of January 1st as the start of the new year for consular service was established by the Romans around 153 B.C. Julius Caesar kept January 1st as New Years day when he instituted his Julian calendar in 45 B.C. We in the West have adhered to this New Years date for over 2000 years, long after the Roman consular service ceased to exist. (Bureaucracies may die but their influence lives on.)
Jewish New Year
Rosh Hashanah (literally, head of the year) is a fall New Years and was observed on September 21, 2009.
Chinese New Year or Lunar New Year (also Korean, Japanese, and Vietnamese New Year)
Chinese New Year usually falls on the second new moon after the winter solstice. For this year, the date is February 14, 2010 (year of the tiger).
Persian New Year
Nowruz marks the first day of spring and the beginning of the year in the Iranian calendar. It is celebrated on the day of the astronomical vernal equinox, which usually occurs on March 21.
Indian New Year (various)
Most parts of India observe a spring New Year around April 14th. Other parts (especially the Gujarati area in the northwest corner of India) observe a fall New Year in October/November.