i) births and deaths

21 January 1978: death of Geoffrey Orme, who wrote The Underwater Menace (Second Doctor, 1967).

21 January 1980: birth of Sarah Dollard, who wrote Face the Raven (Twelfth Doctor, 2015) and Thin Ice (Twelfth Doctor, 2017).

21 January 1993: death of David Blake Kelly, who played the captain of the Mary Celeste in The Chase (First Doctor, 1965) and innkeeper Jacob Kewper in The Smugglers (First Doctor, 1966).

ii) broadcast anniversaries

21 January 1967: broadcast of second episode of The Underwater Menace. The Doctor causes a power cut and Ara rescues Polly. Zaroff explains that he intends to destroy the Earth.

21 January 1978: broadcast of third episode of Underworld. The Trogs rebel against the Guardians; the Doctor and Leela prepare to infiltrate the Citadel.

(Two particularly duff episodes today, in my opinion.)

iii) date specified in canon

21 January 1941: the Doctor and Rose trace a mauve alert to London and meet Captain Jack Harkness, as seen in The Empty Child (2005). Meanwhile the real Captain Jack Harkness is killed in combat. (Torchwood, Captain Jack Harkness, 2007)