When the NRA worked with Congress to establish the NICS, there was specific language in the law that prohibited the FBI from retaining the information on background checks.
If the Feds wanted to trace a specific gun used in a crime, they would go to the manufacturer with the serial number, who would then tell the Feds that they sold that gun to Shotgun Joe's Gun Emporium. The Feds would then go to Shotgun Joe's and he would look up the serial number of that firearm, and he would then pull the 4473 that you signed and say "yup, I sold it to The Rhinelander."
Right now, there is no way for the Feds to call up your name and get a list of all firearms you own. After the "universal background check" law is passed, which also has a provision to authorize the establishment and maintenance of a national gun registry database, the Feds will then be able to punch in "The Rhinelander" and get back a list of all guns you purchased.
That being said, many states do run such a registry, including my state of Michigan who registers handguns. Some states such as New York register all firearms.
That’s good to know, I was not aware of that.