There are a few options, but all of them require purchasing or writing an external application that handles the actual data transfer to the DB.
1. The traditional method - submit the data to a server script that writes/retrieves the data to/from a DB on the server. This one is platform independent.
2. Write a plug-in to connect to a local DB and export the data.
3. Use VB, C#, etc. to write an app that connects to Acrobat through the IAC and writes the data to a local DB.
Not recommended option:
4. Convert your form to LiveCycle and use the built-in LiveCycle DB connection.