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.
In many European countries March 1 or dates thereabouts were historically considered to be the beginning of the year. The names of some months reflect this: September (Seventh), October (Eighth), November (Ninth), December (Tenth). This was originally a Roman habit; but was also encouraged by Christianity, since January 1 was associated with pagan festivals.
The Chinese New Year, is generally celebrated with fire-crackers, and in some localities with a parade.