Is there a website to find out the history of a gun by its serial number?

Depends on the gun. Both the Ruger and Browning websites (under customer service) have a list of serial number ranges for year of manufacture for different models. Sites such as proofhouse have links to many. However, there are thousands of makes of firearms, and there is no ONE site that covers them all- and there is no information from some makers. If you can be more specific (make and model) WE can be more specific.