25 December 1916: birth of Edward Burnham, who played Professor Watkins in The Invasion (1968) and Professor Kettlewell in Robot (1974-75)
25 December 1984: birth of Georgia Tennant, daughter of Peter "Fifth Doctor" Davison and married to David "Tenth Doctor" Tennant; she has played Jenny, the Doctor's daughter, in The Doctor's Daughter (2008), Cassie Rice in animated story Dreamland (2009), Tanya in Big Finish audio Red Dawn (2000) and Alice in Big Finish audio City of Spires (2010), and was the producer of The Five(ish) Doctors Reboot (2013). She and her husband hosted an awfully fun online quiz one evening last week.
25 December 1988: death of Terence Dudley who directed Meglos (Fourth Doctor, 1980) and wrote Four to Doomsday (Fifth Doctor, 1982), Black Orchid (also Fifth Doctor, 1982) and The King's Demons (Fifth Doctor, 1983) not to mention K9 & Company: A Girl's Best Friend (1981).
25 December 1999: death of Peter Jeffreys who played the unnamed Pilot in The Macra Terror (1967) and Count Grendel in The Androids of Tara (1978).
25 December 2014: death of Bernard Kay, who played Carl Tyler in the story we now call The Dalek Invasion of Earth (First Doctor, 1964), Saladin in the story we now call The Crusade (First Doctor, 1965), Inspector Crossland and The Director in The Faceless Ones (Second Doctor, 1967) and Caldwell in Colony in Space (Third Doctor, 1971).
ii) broadcast anniversaries
25 December 1965: broadcast of "The Feast of Steven", seventh episode of the story we now call The Daleks' Master Plan. The Doctor and Sara get arrested at a northern English police station, but Steven busts them out; they then get embroiled on the Hollywood set of a silent movie; and the Doctor wishes "a happy Christmas to all of you at home!"
25 December 2005: broadcast of The Christmas Invasion, first full Tenth Doctor story. As the regenerated Doctor arrives in London, the Sycorax invade, but are repelled.
25 December 2005: launch of interactive game Attack of the Graske on the BBC website.
25 December 2006: broadcast of The Runaway Bride, first appearance of Catherine Tate as Donna Noble. Her wedding turns out to be a front for the release of the Racnoss; the Doctor flushes the spiders down the plughole.
25 December 2007: broadcast of Voyage of the Damned, first appearance of Bernard Cribbins as Wilfred Mott, with Kylie Minogue guest starring as Astrid Peth. Max Capricorn has persuaded the captain of the Starship Titanic to crash into Buckingham Palace, but the Doctor prevents them, at the cost of Astrid's life.
25 December 2008: broadcast of The Next Doctor. Back in 1851, the Doctor thwarts an invasion of England by Cybermen, with the help of Jackson Lake and Rosita Farisi. But here's Dervla Kirwan in charge.
25 December 2009: broadcast of The End of Time. The Master is resurrected; the Doctor returns to Earth via the Ood-Sphere and is captured by the Master in time to witness the transformation of the whole of humaity into duplicates of his arch-enemy.
25 December 2010: broadcast of A Christmas Carol. Amy Pond and Rory Williams are trapped on a crashing space liner, and the only way the Eleventh Doctor can rescue them is to save the soul of a lonely old miser. But is Kazran Sardick, the richest man in Sardicktown, beyond redemption? And what is lurking in the fogs of Christmas Eve?
25 December 2011: broadcast of The Doctor, the Widow and the Wardrobe. Christmas Eve, 1941. A mysterious Christmas gift from the Doctor leads the Arwells into a wintry, magical world. Madge must learn how to be braver than she ever thought possible... and that wishes can come true.
25 December 2012: broadcast of The Snowmen. The Eleventh Doctor has retired to Victorian England, where Strax, Jenny Flint, and Vastra assist him. He meets Clara Oswald, barmaid / governess, and they must fight the Great Intelligence as it tries to take over the world.
25 December 2013: broadcast of The Time of the Doctor. Orbiting a quiet backwater planet, the massed forces of the universe's deadliest species gather, drawn to a mysterious message that echoes out to the stars - among them, the Eleventh Doctor. Last appearance of Matt Smith, and first full appearance of Peter Capaldi as the Twelfth Doctor (his eyes were visible in Day of the Doctor).
25 December 2014: broadcast of Last Christmas. Something sinister lurks in an arctic base at the North Pole, and it's beyond even the most terrible, nightmarish creatures the Doctor has faced before. Who ya gonna call? Santa Claus!
25 December 2015: broadcast of The Husbands of River Song. A surgeon is required to remove a diamond from the head of the tyrannical King Hydroflax. It became lodged there due to a ruthless act of thievery gone wrong, and River Song seeks to recover it. The Doctor sees how she acts on her own - and how many other lovers she has had. But their time is running out.
25 December 2016: broadcast of The Return of Doctor Mysterio. The Twelfth Doctor once more faces off with an alien species that wishes to conquer the planet: the Shoal of the Winter Harmony. This time, however, he has more backup than usual, and with a little twist: a real-life superhero called the Ghost.
25 December 2017: broadcast of Twice Upon a Time. As the Doctor nears regeneration, he stumbles on his original self, also refusing to change. It takes a captain, a glass avatar and a familiar face to convince the Doctors the universe still needs them. Last appearance of Peter Capaldi as the Twelfth Doctor. David Bradley guests as the First Doctor. Includes the longest sequence of any TV Who story set in Belgium. (Well, the longer of the two.)
This makes 25 December the date in the year with by far the most broadcast Whoniversaries, a total of 14 (one Old Who and thirteen New Who). I haven't worked out which date comes second.
iii) dates specified in canon
As well as those mentioned yesterday:
25 December 1883: setting of Attack of the Graske (Tenth Doctor, animated game, 2005)