3 July 2001: death of Delia Derbyshire who arranged Ron Grainer's theme tune to make it as we knew it from 1963 to 1979. See sueworld2003's tribute.
ii) broadcast anniversaries
3 July 1965: broadcast of 'The Watcher', the first episode of the series we now know as The Time Meddler, with newly acquired companion Steven fainting on the Tardis floor and then refusing to believe that they are in 1066. Features the First Doctor picking up a Viking headpiece and asking, "What do you think this is? A space helmet for a cow?" One of the great episode endings as the Doctor discovers that the chanting monks are actually on a gramophone record and is then imprisoned by a set of bars descending from the ceiling. The Monk is the first fellow member of the Doctor's race we have met since Susan.
3 July 2009: broadcast of Torchwood: The Dead Line, the audio play where Jack spends most of the story unconscious (which is just as well since Barrowman is not a natural at audios) and Ianto gets to tell us how much he loves him; while Gwen and Rhys get cuddly too.
iii) dates mentioned in canon
3 July 2379: The date on which the Sixth Doctor story Mindwarp is set, ending with Peri's brain being destroyed - or so we are led to believe. (1986)