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.
Nightingale: The melodic song of this bird has made it a symbol of yearning, love, and death. 1  A little bird told me. 2  I wanna fly like an eagle. 3  The falcon cannot hear the falconer.  Heâs a 1  chicken. He dresses like peacock.  Theyâre acting like 1  vultures! Twitter & tweets!!