DURING the Middle Ages in Western Europe, authorities moved New Year's Day, depending on locale, to one of several other days, including March 1, March 25, Easter, September 1, and December 25. Since then, many national civil calendars in the Western World and beyond have changed to using one fixed date for New Year's Day, January 1 — mostly doing so when they adopted the Gregorian calendar. (Wikipedia)

Some cultures also observe New Year's Day according to their traditions and their calendars that are movable — Chinese New Year, Islamic New Year, Tamil New Year (Puthandu) and Jewish New Year.