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.
Although falconry declined as the use of firearms became more popular in sport and hunting, thereâs no reason why men canât enjoy the sport today. Birds of Falconry. Peregrine Falcon. Falconry utilizes a wide array of raptors. The most well known bird in falconry is probably the peregrine. The peregrine is the fastest animal on earth, capable of diving at speeds above 200 miles per hour. (Take that, cheetah!) Most beginners start with either a kestrel or a red tail hawk.