This website has a bunch of freeware tools that can prevent heart attacks caused by a dying hard drive. I'm using the Unstoppable Copier and it's working great! It copies files so fast and tries to recover corrupted files, which you can skip. It copied 14 Gigs of data in under 10 minutes (I didn't time it, but it was fast).
Here's the official application description:
Recovers files from disks with physical damage. Allows you to copy files from disks with problems such as bad sectors, scratches or that just give errors when reading data. The program will attempt to recover every readable piece of a file and put the pieces together. Using this method most types of files can be made useable even if some parts were not recoverable in the end.
Now, I need to come up with a backup strategy so I don't have to go through this again.