21 September 1960: birth of Sue Vertue, producer of The Curse of Fatal Death, daughter of Terry Nation's agent Beryl Vertue and married to later Who show-runner Stephen Moffatt.
21 September 2010: death of Geoffrey Burgon, who composed the memorable incidental music for Terror of the Zygons and The Seeds of Doom, and also the music for Monty Python's Life of Brian and much else besides. For his birthday I linked to the Terror of the Zygons music; here's The Seeds of Doom.
ii) broadcast anniversaries
21 September 1968: broadcast of second episode of The Mind Robber. Jamie turns into someone else with the same name; team Tardis meet Lemuel Gulliver and end up being charged by a unicorn.
21 September 1986: broadcast of third episode of Time and the Rani. Yet more running around with the Doctor ending up plugged into the machine which will drain his brain.
iii) date specified in-universe
21 September 2360: The Doctor's first, or maybe also last, date with River Song.