25 January 1943: birth of Ian Collier, who played Stuart Hyde in The Time Monster (Third Doctor, 1972) and Omega in Arc of Infinity (Fifth Doctor, 1983), and reprised the role of Omega in Big Finish Productions' excellent Fifth Doctor audio Omega (2003).
25 January 1950: birth of Christopher Ryan, who played Lord Kiv in Mindwarp (1986), General Staal in The Sontaran Stratagem / The Poison Sky (2007) and Commander Stark in The Pandorica Opens (2010). Also played Mike Thecoolperson in the Young Ones.
25 January 1962: birth of Emma Freud, script editor for Vincent and the Doctor (Eleventh Doctor, 2010).
25 January 2017: three days after his 77th birthday, death of Sir John Hurt, who played the War Doctor (The Day of the Doctor, 2013).
ii) broadcast anniversaries
25 January 1964: broadcast of "The Ordeal", sixth episode of the story we now call The Daleks. The Doctor and Susan sabotage the Dalek machines but are captured; Ian is endangered in a very literal cliff-hanger.
25 January 1969: broadcast of first episode of The Seeds of Death. The Ice Warriors take over the Moonbase which controls the T-Mat transport system; meanwhile the Doctor, Jamie and Zoe land in a museum of spaceships.
25 January 1975: broadcast of first episode of The Ark in Space. The Tardis lands on a deserted space station to find booby traps, dead giant insects, and frozen people. (A particularly excellent one this, with nobody other than the new Tardis crew visible and speaking.)
25 January 1982: broadcast of third episode of Four to Doomsday. Monarch's mad scheme to destroy the Earth and make himself God is revealed, and the Doctor is threatened with decapitation.
25 January 1983: broadcast of third episode of Snakedance. Nyssa releases the Doctor, but meanwhile Lon and Tegan have ensured that the Great Crystal will be reinstalled; and the Doctor and Nyssa are captured again. And yes, that is a very young Martin Clunes.
Edited to add: 25 January 2010: broadcast of The Korven, third episode of the Australian K9 series. Starkey is homeless so K9 and Jorjie try to help. Meanwhile, the Korven kidnaps Professor Gryffen. Darius, K9, Starkey and Jorjie must try to save him.