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 Ghost Dance is a Native American spiritual dance done with the purpose of regaining the life once known to the tribe. It is characterized by a revival of many traditional beliefs and by the fervent expectation that a time of perpetual bliss was immanent. Wovoka, a Paiute, was born in western Nevada around 1856.