- 406 80,000 Vandals, Alans and Suebians cross the Rhine at Mainz, beginning an invasion of Gallia.
- 1775 Battle of Quebec in American Revolutionary War; Americans defeated trying to take British stronghold
- 1861 22,990mm of rain falls in Cherrapunji Assam in India in 1861, a world record
- 1904 The first New Year's Eve celebration is held in Times Square, then known as Longacre Square, in New York, New York.
- 2004 The official opening of Taipei 101, the current tallest skyscraper in the world, standing at a height of 509 metres (1,670 feet).
English astronomer James Bradley announces discovery of Earth's nutation motion (wobble)
On December 31, 1744