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.
A hummingbird is the only bird able to fly backwards (under its control). It is not aerodynamically possible for most birds to fly backwards. However, some are able to turn somersaults or cartwheels in mid-air, as a means of better pursuing or catching their prey. One example of this is the Roller Pigeon, which uses the technique to catch insects in flight.