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.
The Rainbow Lorikeet is earned itâs name because almost every color of the rainbow are found on the feathers. The Rainbow Lorikeet have a surprising long lifespan of over 20 years. The Peacock is of the pheasant family and the male is one of the most colorful birds in the world. The males are famous for displaying a fan of feathers to attract a mate. The Golden Pheasant while a bird of beauty is often hunted for sport.