The family register is referred to as the koeski. There isn't really any comparable thing in the U.S. unless you want to consider genealogy trees.
A family register is basically a requirement of living in Japan.
These are also matters of public records so anyone can examine them. This includes employers and prospective mates. If there seems to be a good chance of a marriage taking place, for example, the parents will consult the family register to make sure there is nothing really bad about the person such as being a member of the Burakumen or the outcast class of Japanese society.
I can also see, though, where such a thing would be of great value in determining just who one's ancestors actually were depending on how far back the registries go. Unfortunately many have been lost over the years due to fires.
Japan main page
Japanese-American Internment Camps index page
Japan and World War II index page