The waltz was a common style of ballroom dance on Earth. The Sixth Doctor met a woman named Becky, from whom he learned the dance. Some 80 years later in his own life, he met Becky as a teenager and taught her how to waltz, effectively meaning that he had taught himself the dance. (PROSE: Teach Yourself Ballroom Dancing)
The Eighth Doctor stated that he had not gone waltzing in ages. (AUDIO: The Silver Turk)
When Audacity Montague was injected with a full vial of Dextro-7 to wake her up, thereby preventing her from being taken over by the Mara, she arose in a state of delirium, desperate to move, constantly giggling, and pressuring the Eighth Doctor into waltzing with her. (AUDIO: The Gloaming)
Later, while disguised as John Smith by the chameleon arch, the Doctor attended a local dance and attempted the waltz with a very forgiving Joan Redfern. (TV: Human Nature)
In an alternate timeline in 1963, created by Maestro draining music from the Earth, Paul McCartney told the Fifteenth Doctor that bad songs were how things should be, that it wasn't like the old days when they had waltzes and fandangos. (TV: The Devil's Chord)