How to recover data from a failing hard drive? [duplicate]

An external 3½" HDD seems to be in danger of failing — it's making ticking sounds when idle.

I've acquired a replacement drive, and want to know the best strategy to get the data off of the dubious drive with the best chance of saving as much as possible.

There are some directories that are more important than others. However, I'm guessing that picking and choosing directories is going to reduce my chances of saving the whole thing. I would also have to mount it, dump a file listing, and then unmount it in order to be able to effectively prioritize directories. Adding in the fact that it's time-consuming to do this, I'm leaning away from this approach.

I've considered just using dd, but I'm not sure how it would handle read errors or other problems that might prevent only certain parts of the data from being rescued, or which could be overcome with some retries, but not so many that they endanger other parts of the drive from being saved. I guess ideally it would do a single pass to get as much as possible and then go back to retry anything that was missed due to errors.

Is it possible that copying more slowly — e.g. pausing every x MB/GB — would be better than just running the operation full tilt, for example to avoid any overheating issues?

For the "where is your backup" crowd: this actually is my backup drive, but it also contains some non-critical and bulky stuff, like music, that aren't backups, i.e. aren't backed up.

The drive has not exhibited any clear signs of failure other than this somewhat ominous sound. I did have to fsck a few errors recently — orphaned inodes, incorrect free blocks/inodes counts, inode bitmap differences, zero dtime on deleted inodes; about 20 errors in all.

The filesystem of the partition is ext3.