9 August 1920: birth of Graham Leaman who played four roles in five Old Who stories: the captive Controller in The Macra Terror (1967), Price the communications office in Fury from the Deep (1968), the Grand Marshall of the Ice Warriors in The Seeds of Death (1969), and an un-named Time Lord in Colony in Space (1971) and The Three Doctors (1973). (Some dispute whether it is actually the same Time Lord.)
9 August 1931: birth of Alethea Charlton who plays Hur in An Unearthly Child (First Doctor, 1963) and Edith in The Time Meddler (First Doctor, 1965). Here she is from the same angle in both stories.
9 August 1940: birth of Bernard Holley, who plays Peter Haydon in Tomb of the Cybermen (Second Doctor, 1967) and the voice of Axos in The Claws of Axos (Third Doctor, 1971)
9 August 1953: birth of Roberta Tovey who plays Dr. Who's granddaughter Susan Who in the two Peter Cushing films, and also recorded a justly forgotten single, "Who's Who".
9 August 1968: birth of Sanne Wohlenberg, producer for three Eleventh Doctor stories in 2010-11.
ii) webcast anniversary
9th August 2002: webcast release of the second episode of Real Time, in which one of the scientists has been transformed into a Cyberman and they all try to acquire the Tardis.
iii) dates specified in-universe
9 August 1794 is when the Doctor and disposable Time Lord companion Serena arrive in revolutionary France in Terrance Dicks' 2005 Second Doctor Season 6B novel, World Game.
9 August 1932 and 9 August 1945 are critical dates for the character Rita Hay in Mike Tucker and Robert Perry's 2003 Seventh Doctor novel Loving the Alien, the first being the day she was born and the second her 13th birthday when the UK used an atomic bomb (in a slightly divergent history of course).