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:
There is a setting inside the PDF file that turns on the allow saving with data bit. However, it requires that you have a copy of Adobe Acrobat installed to change the bit.
The only other option is to print it to a PDF print driver which would save the data merged with the pdf file.
UPDATE: The relevant information from adobe is at: http://www.adobeforums.com/webx?13@@.3bbb313f/7