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.
Also the Goddess Ba is often portrayed as a bird. For more information on Ba and other feathered creatures please go to the Feathered Creatures page. Also the Shuti, two feathers symbolizing light and air, can be found on the heads of many Egyptian Gods. This symbol has mostly been made out of gold and semiprecious stones.