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.
Like all birds of prey, eagles have very large powerful hooked beaks for tearing flesh from their prey, strong legs, and powerful talon claws. The eagle is the mascot of Ravenclaw House at Hogwarts School of Witchcraft and Wizardry. The body of a Hippogriff is half-eagle and half-horse. Eagle feathers are sometimes used for quills. On Christmas in 1992, Hermione Granger presented Harry Potter with a luxury eagle-feather quill as a Christmas present.