As said before, ddrescue is a really great data rescue utility. I've made a really simple AS application wrapper for it. Just name the applet, for example, “ddrescue-disk2s3”, copy it on your backup drive, launch and give sudo your password.
It functions just like the shell snippet I, but contains the ddrescue binary so it's super easy to move around, also you don't have to edit any text files - just put the failing drive's /dev name in the app name.