Yes. This is something I'd wanted to do for a long time and just stumbled onto by accident.
You can't do it with just the reader, you have to have full acrobat. I'm looking at version 4.
There are some icons across the top and some down the left side of my screen. When I download a document and open it,
The hand at the top of the left column is highlighted.
Look down the left side. At the bottom is a T. Above that is a hand holding a pen. Above that are two funny looking superimposed squares. Click on that. Move the mouse back out to the document. You'll see a cross hair. Put that on the lower left corner of a field you want to fill in and draw a box. Then answer the field properties questions. Repeat as necessary. When you're ready to fill in, click back on the hand. Back on the document the hand will change to a vertical line when it is over a box you've created.
I have downloaded several State Quarterly unemployment PDFs and made them into completable forms this way.
Help-user guide-using and creating pdf form chapter for more help.
Dave