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.
Song bird and other exotic bird feathers are prized by Native American for certain characteristics. The feathers of blue jays, cardinals, and some other brightly colored birds are used for their medicine by spiritual leaders. Medicinal teas are made by steeping or boiling particular feathers in water.