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.
Even through binoculars there was no question about this bird's identity: Buff-bellied Hummingbird. When the hummer finally entered the trap at 8:30 a.m., Hilton pulled the string and had a new record for South Carolina--the first Buff-bellied Hummingbird ever seen or banded in the state. As implied by its species name, Amazilia yucatanensis, the buff-bellied is a bird of Mexico's Yucatan region, with a year-round range from the Yucatan peninsula northward along the Gulf Coast to south Texas.