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 Sun Dance was the most spectacular and important religious ceremony of the Plains Indians of 19th-century North America, ordinarily held by each tribe once a year usually at the time of the Summer Solstice.uring the Sun Dance the eagle is the facilitator of communication between man and spirit. The Crow may be accompanied by a dancing eagle in his visions, the eagle instructing him about the medicine acquired through the vision. The eagle's feathers can cure illnesses.