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.
1 Groups of cowbirds are known as a herd or corral.. 2  In the winter, brown-headed cowbirds join several other species of blackbirds to form large roosts, numbering well in the thousands. 3  Their song is characterized by a somewhat gurgling glug-glug-glee tune.4  They are very noisy birds. Groups of cowbirds are known as a herd or corral.. 2  In the winter, brown-headed cowbirds join several other species of blackbirds to form large roosts, numbering well in the thousands. 3  Their song is characterized by a somewhat gurgling glug-glug-glee tune.