Last week some family members suffered a corrupted hard drive on their only PC. They had no backup. They're relatively light computer users--no online banking, no important business documents--but the lesson still hurts. Their e-mail contacts weren't too hard to recover--they simply called everybody they had regular e-mail contact with and told them to send an e-mail. Their digital photos are gone forever, unless emergency tech support courtesy of their son-in-law produces a miracle. And their music library?
That's one nice thing about having a large-capacity MP3 player: if you're lazy about backup, at least you still have all (or most) of your tunes. The easiest solution for iPod users, in my opinion, is to use a utility like Music Rescue (I used it back when it was called iPod Util and highly recommend it) or 4Media iPod to PC Transfer for a Windows PC, or Senuti for Mac. Follow the instructions carefully--you don't want iTunes on your new replacement PC to try and automatically sync its (empty) library to your (full) iPod or you'll overwrite all the songs in their last remaining location!
If you don't mind improvising a bit, this CNET tutorial from 2006 describes how to set up your iPod as an external drive in Windows XP, although you'll have to skip step 1 if your original PC is dead. (Steps 3 and onward should work for many other MP3 players as well.) Apple has also posted instructions for moving songs from an iPod to a Mac or PC, but again they assume that the computer with your original library on it is still working.
If you're among that minority of users who bought a Zune player from Microsoft, it has a pretty straightforward reverse sync process.
Of course, the most important lesson to learn is backup, backup, backup. If you've got a few GB of files you just don't want to lose, an inexpensive flash drive or online service (I use Microsoft's SkyDrive, which has a 5GB capacity and is free) is probably fine. External hard drives are for large amounts of critical data--like if you're building multitrack recordings. If you want backup and restore--that is, the ability to restore everything on your computer to the way it was, not just recover lost data--then you'll need disk imaging software for PC or an equivalent Mac solution.