The military records website Fold3.com had started digitizing the WWII navy muster rolls for the period 1939-1949. Although Fold3 is a fee site, this set of records is free. This periodic list of the personnel on a ship can prove a valuable souce of information about their movement/assignments and more.
The documents can be searched by name or by ship name. So if you know the name of the ship your ancestor severed on, you can easily check the rolls. To do that click on the "Records" tab at the top of the home screen and select "Browse Records." Then click on "World War II" and "WWII Navy Muster Rolls" on the next two lists that appear. The next list is where you select the name of the ship and then you can see the rolls. They are organized alphabetically by surname.
The digitizing project is on-going so it is worth while checking back often as new records are added.
Check it out at http://www.fold3.com/