I've tried dragging using the box tool, and then fill, but this doesn't work. Is there a way to specify an area to be blacked out completely on a page so that it is rendered unreadable?
IF you have Acrobat 9 go to advanced menu. then to Redaction menu. I belive that will do what you want. I've never used it so I have no idea how it works.
(Please note information is given by an Experienced User of Acrobat. I am not an employee of Adobe.)
To add to Phillips comments, you can do that in version 8 Pro or 9. It wasn't available in older versions.
Go to Advanced>Redaction>Show redaction toolbar. Choose "redaction properties" and you can tell it what to do. Then you use the mark for redaction tools to select your area or text and then choose "apply redactions".
Keep in mind that this is permanent and cannot be undone.