This is a historical problem with Acrobat, goes way back. To do this you **used** to have to have an enterprise (or professional?) version of Acrobat, and every user that would read the saved PDF's would have to have a copy, requiring a multi user license. Very spendy.
You can, however, use Standard to create form controls and submit the data to a URL. As mentioned above, some of that may have changed. I think the world has moved on to more cooperative tools for collecting form data.
My understanding is that Adobe Reader can, since I don't know what version, submit completed forms. You need a submit button or whatever, and it e-mails the data. It does this by opening the e-mail client with a new message to your specified address with the data file attached. The recipient can then plug this into the original file to see the data. A bad joke of a database client if you ask me and a horrible submission mechanism. Better to set something up on your website if you're dependent on the internet for returns anyway.
The link above says you can give Reader 8 + the right to save the PDF with the completed form fields. I'm fairly sure this is a distinct function to just returning the data.