I just bought my first AR-15, a pre-ban.  When I picked it up from my local gun shop I filled out a form that asked for name, social, serial number etc.  They also called someone to give them my name and social and gun serial number.  What happens to the form that I filled out and what happens when the dealer gave my name and a serial number?  Is there a database somewhere that will always know that I am the owner of that gun?  

The call was to the FBI's national instant check system (NICS), or your state's point of contact for that system, if applicable.

The check data is supposed (by law) to be purged from the system after the check has been completed, but the Reno justice department has allowed the FBI to retain that data (supposedly) for a period of six months for 'statistical' information gathering.  Federally, the serial number and types of weapons are not reported - although individual states may require this information.  From your description, I guess your state collects the weapon's serial number and saves that information, since it's not required for the NICS check itself.

The city in which I live and do business (Colorado Springs, CO) requires me to send in a record of all sales, which includes all your personal information, weapon type and serial number, which the city police maintain in their records basically forever.

Your personal information on the 4473 (yellow sheet) is retained in the dealer's records for at least 20 years.  Upon discontinuance of that dealer's business, all records still on file will go the ATF's out of business records center where they'll probably also stay on file forever.

damn, you are one paranoid man... ;)