The most common modern celebrations are:
January 1 : Western cultures that start a year with January.
[Rosh Hashannah]? (Hebrew for 'head of the year') is a celebration that is 163 days before Pesach (Passover). (See Hebrew Calendar). In the Gregorian calendar at present, Rosh Hashannah cannot occur before September 5, when it occurred in 1899 and will occur again in 2013?. After the year 2089?, the differences between the Hebrew Calendar and the Gregorian Calendar will force Rosh Hashannah to not be earlier than September 6. Rosh Hashannah cannot occur later than October 5, when it occured in 1967 and will again occur in 2043?.
The [Roman Catholic church]? would start their ecclesiastic year on a principal Christian feast, like Easter or Christmas. This used to be followed in the past by many European administrations.
An ancient Roman tradition had the year start on March 1, which is still reflected in the names of some months which derive from Latin numerals: September (Seventh), October (Eighth), November (Ninth), December (Tenth). An (apparently) later convention had the year start 2 months earlier, and named the month after Janus, the 2-faced (forward- and backward looking) god of gates and transitions in general.
The Chinese new year is generally celebrated with fire-crackers, and in some localities with a parade. It falls at a new moon during the (Chinese) winter.