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.
They are known as hummingbirds because of the humming sound created by their beating wings which flap at high frequencies audible to humans. They hover in mid-air at rapid wing-flapping rates, typically around 50 times per second, allowing them also to fly at speeds exceeding 15 m/s (54 km/h; 34 mph). Hummingbirds have the highest metabolism of any homeothermic animal.