Any ship worldwide from which we have ever received an AIS message can be found in the FleetMon Vessel Database. This includes for example the global merchant fleet of cargo ships and tankers, all kind of offshore and supply ships, tugs, passenger ships, pleasure crafts and sailing vessels, fishing ships and many more:
You can use the quick search on the top left of the website to search for ships by name, IMO number, MMSI number or by call sign.
Also, you can open the vessel database at http://www.fleetmon.com/vessels and search for the ships of your interest, using additional filters like flag, vessel type, dimensions and deadweight.
In case you still can not find the ship you are looking for, please get in contact with the support team.