Yes it does happen, however as Peter said you need to have some idea of who the person is.
It's only really used when the body has suffered from such trauma that visual identification is not possible, that could either be due to fire damage, decay or external damage.
Normally in those cases all the police have to go on are bones and teeth, the bones will identify the sex and likely age of the person but nothing more (unless they have a specific indicator like a break).
The usual course of action would be to establish who the likely victim was based on location, time of death and a list of relevant missing persons, then checking their dental records for a match.