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.
Pan Pat, Myanmar-Women of the Kayan tribe in Myanmar are well known for wearing brass coils around their necks their entire lives in order to lengthen it. The belief is the longer the neck, the more beautiful the woman. The cultural practice does have its drawbacks.