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.
As far as birds go, hummingbirds are among the most territorial of all. They have been known to claim an entire flowerbed as their own, and even lay claim to three or more feeders, flying from one to another over and over again to chase away any who dare enter âtheirâ territory. They have been known to defend an area up to a quarter acre in size.