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.
Hopi Snake Dance-The most widely publicized of Hopi rituals was the Snake Dance, held annually in late August, during which the performers dance with live snakes in their mouths.The dance is thought to have originated as a water ceremony because snakes were the traditional guardians of springs.opi Snake Dance-The most widely publicized of Hopi rituals was the Snake Dance, held annually in late August, during which the performers dance with live snakes in their mouths.