i) broadcast anniversaries
23 December 1967: broadcast of first episode of The Enemy of the World. The Doctor, Jamie and Victoria land on a near-future Australian beach, are attacked by gunmen, rescued by Astrid in her helicopter, and discover that the sinister Salamander is the Doctor's double.
23 December 1978: broadcast of first episode of The Power of Kroll. In search of the fifth segment of the Key to Time, the Doctor and Romana land on the third moon of Delta Minor, where Romana is captured by the native Swampies and the Doctor by the protein miners.
ii) date specified in-universe
23 December 1892: The Eleventh Doctor meets Victorian barmaid Clara Oswald in London, as seen in The Snowmen (2012).