Whether they have any extant function or not, they have lost their former function and in that sense they do fit the definition of vestigiality. Vestigial structures are often called vestigial organs, although many of them are not actually organs.
There are quite a few birds famous for doing ritualized mating dances, so I would only list 5: The Red Capped Manakin, The Black-footed albatross, The Western and Clark's grebe, The Superb bird of Paradise, & The Victoria's riflebird.
In magical symbology the bluebird represents confidence. And in the Valentine myth, the Bluebird is a 'man of laughter' and symbolizes happy love. Because of its benign qualities, it has become a favourite subject in European fairy tales -- and song. 'The Bluebird of Happiness' became a popular song in the 1940's.