i) births and deaths
20 June 1929: birth of Paul Bernard, who directed Day of the Daleks (Third Doctor, 1972), The Time Monster (Third Doctor, 1972) and co-directed Frontier in Space (Third Doctor, 1983).
ii) broadcast and publication anniversaries
20 June 1964: broadcast of "Strangers in Space", first episode of the story we now call The Sensorites. The Tardis lands on a spaceship whose crew have been incapacitated by the mysterious Sensorites.
20 June 1970: broadcast of seventh episode of Inferno, ending Season 7 of Old Who; last regular appearance of Caroline John as Liz Shaw. The Doctor and Liz prevent the drill from breaking through the crust; Stahlman is completely transformed into a Primord and is restrained.
20 June 1991: publication of Timewyrm: Genesys by Terrance Dicks, first in the run of New Adventures published by Virgin.
20 June 2007 or 2008: setting of the 2008 Torchwood episode, To the Last Man.
There’s also the classic Blackadder line “Baldrick, you’ld laugh at a Shakespeare comedy”