I have been waiting for a decent free file manager to come to the BlackBerry PlayBook. AIR Browser is trying to fit that bill with a pretty solid file manager though it does have some quirks. You can copy, paste, and rename your shared files through the app and it does a pretty nice job of it. It could use some refinement and the ability to open attachments but all in all a pretty nice app by Nicolas CHAIX.
You can find AIR Browser in App World at this link or simply search for it from your PlayBook!