21 May 1953: birth of Trevor Cooper, who played security chief Takis in Revelation of the Daleks (Sixth Doctor, 1985) and Friar Tuck in Robot of Sherwood (Twelfth Doctor, 2014)
21 May 1985: birth of Calvin Dean, who played the Slitheen in the form of a boy called Chris in The Gift (Sarah Jane Adventures, 2009) and security guard Ha-Ha in Nightmare in Silver (Eleventh Doctor, 2013).
ii) broadcast anniversaries
21 May 1966: broadcast of "The O.K. Corral", last episode of the story we now call The Gunfighters, and the last episode before 2005 to have an individual title. Doc Holliday and the Earps shoot it out with the Clantons, to the detriment of the latter. NB that Doc Holliday and Kate Horony are the last two historical characters to be depicted in TV Who until George Stephenson in Mark of the Rani (1985), 19 years later.
21 May 2005: broadcast of The Empty Child; first appearance of Captain Jack Harkness and first contribution to New Who by Steven Moffat. The Doctor and Rose find London in the Second World War infested by zombies with gas-masks.
21 May 2011: broadcast of The Rebel Flesh. The Doctor must mediate between the original workers at an acid-mining factory, and their rebellious artificial duplicates.
iii) date specified in-universe
21 May is a crucial date in the plot of The Ghosts of N-Space (Third Doctor audio, 1996).