None. There's quite enough for today as it is.
ii) broadcast anniversary
31 December 1965: broadcast of third episode of The Highlanders. Polly overpowers Ffrench; the Doctor overpowers Perkins; but Ben is thrown into the cold sea...
iii) dates specified in canon
31 December 1879: Queen Victoria issues the Torchwood Charter, as seen in Children of Earth (2009). (Though it must be a fake since she is referred to inaccurately as 'HRH', ie 'Her Royal Highness', rather than 'Her Majesty'.)
31 December 1930: setting of the framing narrative of the 2002 Eighth Doctor / Charley audio, Seasons of Fear, by Paul Cornell and Caroline Symcox.
31 December 1965 (?) setting of end of "Volcano", the eighth episode of The Daleks' Master Plan.
31 December 1986: setting of Paul Grice's short story "Mondas Passing", featuring Ben and Polly, included in the very first BBC Short Trips anthology.
31 December 1999: setting of most of Doctor Who: The Movie.
also 31 December 1999: setting of most of Craig Hinton's 1995 Sixth Doctor / Mel novel, Millennial Rites.
also 31 December 1999: setting of Gareth Roberts' 1994 DWM comic strip story featuring the Seventh Doctor and Mel, Plastic Millennium.
also 31 December 1999: Torchwood Three wiped out (apart from Jack Harkness) in a multiple murder / suicide by its leader Alex Hopkins (as shown in the 2008 episode Fragments).
also 31 December 1999: Setting of Mark Magrs' 2009 Iris Wildthyme audio play, The Panda Invasion.
31 December 2004: Rose Tyler misses a New Year's Eve party and bumps into this odd bloke wearing a suit and sneakers on her way home, as seen in The End of Time II (2010).
31 December 2599: setting of part of Justin Richards' 2000 novel The Doomsday Manuscript, first in the Big Finish series of Bernice Summerfield books.
31 December 4999999999: setting of third issue of the 2008 IDW Doctor Who comic, written by Gary Russell, in the series which has been retrospectively named Agent Provocateur.