10 December 1921: birth of Anthony Coburn, writer of the very first Doctor Who story, An Unearthly Child (and also of the unbroadcast The Masters of Luxor).
ii) broadcast anniversaries
10 December 1966: broadcast of sixth episode of The Power of the Daleks. The Daleks start to take over but the Doctor manages to overload their circuits and destroy them.
10 December 1977: broadcast of third episode of The Sun Makers. Leela is captured and is to be executed by steaming (a particularly gruesome fate).
10 December 2006: broadcast of Random Shoes (Torchwood), the one with Eugene the dead guy and the alien eye.
iii) dates specified in canon
10 December 1981: Sarah Jane Smith fails to pick Brendan Richards up from school. (K9 and Company).
10 December 1983: Bernice Summerfield is reunited with her father. (In Kate Orman's Return of the Living Dad, published 1996; there are a number of Orman novels with dates specified in December.)