If you have ever dealt with a corrupted hard drive you have come across this problem. You are trying to move files from the old/corrupted hard drive and as you are copying you hit a bad file. The copy job stops leaving you at a loss for what has copied and what hasn't. I have spend many an hour digging through file lists making sure I copied everything I was able to. Well I had that very same problem today and I decided that someone out there must have solved this problem. Sure enough.
Y-Copy is a great free program that will continue to copy files even if one has failed. It keeps a log of files that have failed so you can let the user know what just didn't make it off the drive.
Note: I first found another application that was supposed to do the same thing. It was actually part of the PC Repair System USB Key (That I wrote about before). Encopy is a good app, but I didn't like the interface or the usability as much as I did Y-Copy. There are many more features in Encopy so if you find Y-Copy lacking in options check it out.