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.
The dance of the seahorse is one of the most beautiful courting behaviours in the ocean. At dawn and dusk, male and female sea horses entwine their tales, breaking off occasionally to âdanceâ by circling each other for up to several minutes at a time.