I’ve personally tried this, using Ubuntu’s Live CD. Basically, you only need to boot into Linux, mount the necessary drives which is usually automatic. They can be portable drives as well which was the case for me when mine refused to get detected in Windows because of mechanical failure. It seems Windows will keep on retrying infinitely, whereas Linux just mounts it without reading the whole drive. Obviously, certain files that resides on the faulty part of the drive will fail to read, but that’s fine - I’ll take losing a couple of files to the entired drive’s content anyday.

For a more step-by-step approach, take a look at Geek to Live: Rescue files with a boot CD - Lifehacker