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 Resplendent Quetzal (Pharomachrus mocinno) has been called the most spectacular bird in the New World (Peterson and Chalif, 1973). The Quetzal was the most sacred symbol of the Aztecs and Mayas.he Quetzal is found on both igneous and limestone terrain where mature or virgin cloud forests occur (LaBastille, et al, 1972). They are generally found between the altitudes of 4000 feet up to 10,500 feet and the forests they inhabit have a canopy of oak trees 100 to 150 feet tall (Skutch, 1944).