How do I enable saving of filled-in fields on a PDF form?

Open your PDF in Google Chrome. Edit the PDF as you want. Hit ctrl + p. Save as PDF to your desktop.

When you use Acrobat 8, or 9, select "enable usage rights" from the Advanced menu. This adds about 20 kb to the pdf.

The other possibility is to use CutePDF Pro, add a submit button and have the XFDF data submitted to your self as an email or to a web server. The XFDF data can then reload the original PDF with your data.

If you are using Adobe Acrobat X to make the form, set all the fields as you want them, then click File, Save As, Reader Extended PDF, Enable Additional Features. The resulting PDF form can be saved when filled in, if opened in versions of Adobe Reader before XI.