In Firefox 1.0.7, go tools->options, and select "privacy" from the left-hand side. From there, click the plus sign next to "saved form information" to expand it, then check the box next to "save information I enter in web page forms and the search bar" and OK your way out.
In Firefox 1.5, the layout of options has been changed a little bit. This time, select "privacy" from the top bar, click the "saved forms" tab, check the box next to "save information I enter in web page forms and the search bar" and OK your way out.