A choir singing without instrumental accompanyment is called an a capella choir. Non-accompanied vocal music is considered a cappella due to restrictions on th use of instruments in medieval churches.
Many standard choral works are a cappella in that no accompaniment is written in except perhaps for rehearsal purposes. But in the modern parlance, it applies to vocal ensembles who disdain instrumental accompaniment in all cases. Barbershop?, [doo wop]?, and [contemporary a cappella]? are some of the major movements within modern a cappella musicmaking.
Famous a capella ensembles: