Some PDF forms can be saved, including all filled-in field data:
Some others can not be saved, and all filled-in field data are lost:
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.
Open your PDF in Google Chrome. Edit the PDF as you want. Hit ctrl + p. Save as PDF to your desktop.
On linux use cabaret stage:
https://www.cabaret-solutions.com/download/caba-lin-64
You can fill and save cleanly
Preview in OS X seems to be able to do this out of the box. Adobe Reader shows the doc as "data typed can't be saved" but Preview was able to save my changes without hassle.
You can use the free foxit reader to fill in the forms, and if you pay a little you can design the forms that way you want.
You can also us iText to programmaticly create those forms.
There are free online services that allow you to upload a pdf and you can add fields also.
It depends on how you want to do the designing.
EDIT: If you use foxit reader, you can save any form that is fillable.
With the latest version of Adobe Reader, Adobe Reader XI, it seems that you can save the form.
From their webpage: Type your responses right on the PDF form, or click through and fill in the form fields. Then save and submit