I have a PureDigital Model 225 Flip. I accidently deleted all the videos on the unit when the recorder showed FULL. Is there any hope of recovering any of them?

I have had success with this flip camera recovery software... Download the program
Camera Video Recovery Software

You have to use a card reader either on your computer or an external USB card reader. Put the card in the card reader, open the recovery program, then select the drive where files are deleted, then press "Next" and wait for it to do it's magic.

You can refer to this guide
Recover files from memory card

You have chance to get back some or all of those lost videos from your Flip Camcorder if you take care.

First things first: DO NOT take any more videos with the memory card or hard disk (on your camcorder) that you want to recover videos from. Take the memory card or disk out of your cam and put it in a safe place. Because if you take any more videos or save any data to your memory card or hard disk, you may quite possibly ruin your chances of video recovery.

Then Connect the card or disk to your computer as it should appear as a "Removable Drive" or put the card in a card reader attached to your PC.

Next, if you are comfortable with using a PC then you can download a data recovery utility that will recover your videos with Wondershare Recovery Software (I once used this program bounded with some other software) from the following link:

Video Photo Recovery (if you are running Windows OS)
Mac Data Recovery (from MacUpdate site)

Remember - Do NOT try & write anything back to your camcoder(card or disk) until you can recover your videos safely!