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.
Popularized in Warner Brothers Cartoons. The legendary roadrunner bird is famous for its distinctive appearance, its ability to eat rattlesnakes and its preference for scooting across the American deserts, as popularized in Warner Bros. cartoons. The roadrunner is a large, black-and-white, mottled ground bird with a distinctive head crest.