Every ship must be listed in one Classification Society. The most reputable are associated in IACS, International Association of Classification Societies.
That Society surveys the ship and certifies to the Authorities in the ports where the ship calls that she has the conditions indicated in the Certificates and can carry out the port operations safely, and that the ship is seaworthy and can sail without danger for her crew or the enviroment.
Nowdays these Societies have several activities, not only related to sea, as you can see in their webs.
Here are the Societies integrated in IACS.
Lloyd's Register of Shipping It is the oldest and the very well known. It was founded in 1760.
Det Norske Veritas It is Norweigian and has plenty ships in its list because there are many ships controlled by Norweigian companies, registered under many different flags, and normally they prefer the Society from their country.
Veritas This is French and has very
strong implatation all around the world.
Lloyd This is German. I have been in Spanish ships classed by them.
Bureau of Shipping Another big one, in this case from USA.
Kaiji Kyokai The Japanese.
As Japan has a very big fleet, normally registered in another countries, her
ships are normally in this Society.
Registro Italiano Navale It
is clear that this is Italian.
of Shipping Korea has an important fleet,
the most of it classified by this Society.
China Classification Society
Russian Maritime Register of Shipping
Hrvatski Registar Brodova
(Croatian Register of Shipping)
Indian Register of Shipping
Polski Rejestr Statokow