Unless the creator of the PDF form has enabled that feature, you cannot save filled-in forms in Adobe Reader X. You either need to use Adobe Acrobat, or contact the forms creator and ask them to send you an extended-rights version which can be saved in Reader.
I have been trying to save a form in Adobe Reader X (it is an online application), but it will not work and when I try to use Adobe e-mail service, it sends the form blank.