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.
Birds hold a sacred spiritual significance, like all animals. The sacred symbolism of birds is seen clearly through observation of the spiritual practices of early African tribes and in Egyptian civilization. These ancient tribes studied the sacred symbolism of birds because they were thought to express the divine will and expression of God. The sacred symbolism of birds is interwoven into the mythology and spirituality of early African tribes. Early Egyptian gods were zoomorphic; this means they had animal characteristics.