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.
Named for its melodic mating call, the piping plover (Charadrius melodus) is a small shorebird, one of several plovers in the Americas that shows a single black neck-band in breeding plumage.amed for its melodic mating call, the piping plover (Charadrius melodus) is a small shorebird, one of several plovers in the Americas that shows a single black neck-band in breeding plumage.