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.
And now two smaller Cratchits, boy and girl, came tearing in, screaming that outside the baker's they had smelt the e the baker's they had smelt the goose, and known it for their own; and basking in luxurious thoughts of sage and onion, these young Cratchits danced about the table, and exalted Master Peter Cratchit to the skies, while he (not proud ...