I don't pretend to have the best backup regime yet, but I didn't even regularly do backups until around 2004. My main system at the time was a PowerMac G3 (Blue/white). I was obliviously going day-to-day with all my primary storage on a single 80GB Maxtor drive (back when it would all fit on such a small drive).
Then suddenly one day the drive started to emit a horrible clicking sound (the dreaded Click of Death). After some attempts to scrub the drive with the lowly Disk Utility (Mac OS's fsck), the drive finally stopped mounting at all. I even tried Disk Warrior but it couldn't do anything with the drive because it wouldn't even mount. In hindsight it wasn't smart to keep doing this, as potentially there was some debris loose in the case that was ripping up the platters. At first sign of trouble, I should have stopping forcing it.
Desperation time. Searches on the Internet yielded various suggestions. One method that seemed to keep cropping up seemed a little strange, but there was enough anecdotal testimonials about it to make it worth trying. After all, the drive couldn't get much deader.
If this attempt was a bust, then worst case would be to either shell out big bucks to a drive recovery service, or just lose the data. Suddenly the cost of NOT doing regular backups came back to bite me. Pay a few hundred up front and be safe, or pay perhaps much more later on and not even be assured of getting all your data back.
Anyway, the last-ditch method I read about was the semi well-known "freezer" trick.