Scan it.  I have gradually shifted from analog to digital with everything I can.  We only have one copy of most of the photos in our family albums.  If those were ever lost in a fire or flood, even the negatives might very likely be lost in the blaze or deluge.  I have a Pentax 600, and that's the easiest scanner on the market for digitizing your photographic history.  It also handles single sheets of paper, so I have also scanned in hundreds of pages of letters.  The obvious advantage of digital is that you can make an infinite number of copies, so I back up the digital versions and distribute them to family and friends.
 

Burn it.  A relatively quick and dirty way to back everything up is on old-fashioned cd- or dvd-roms.  These have the disadvantage that you can't update them as easily as you do the contents or your hard drive, and you also have to do a bit of math to see what will fit on each disc (e.g., your mp3 collection may be spread over several whereas you might be able to fit My Documents with your pics and other miscellany).
 

Image it.  One of the best investments I ever made was an external hard drive.  I only plug it in long enough to back up the entire hard drive (except for system and program files since those would need to be freshly installed in the case of a crash, so why bother?).  I started off with a 180MB external drive which was more than enough to accommodate everything I needed from my 120MB hard drive a couple times over... so I was able to save subsequent back-ups concurrently.  Over time I had to upgrade, so I went with a 500MB external (contrast with my 200MB hard drive at the moment).  Want to know what I did with the original external HD?  Read on.
 

Bank on it.  Like I said, Hurricane Katrina made me realize that an entire home (or subdivision even) could be lost.  It didn't matter that I backed everything up if the backups were lost with the CPU.  After I used the external drive to image the contents of the computer, I put it someplace safe from theft or damage: in the bank.  Maybe a safety deposit box is going a bit overboard, but it's cheaper even than insuring the computer.  Now, short of perhaps a nuclear strike, everything should be secure from any event that would affect the computer itself.  I keep the larger hard drive at home and update that regularly whenever I'm about to do anything significant to the computer (for fear I'll have to do a clean install if something goes awry).  The safety deposit box is a less-frequent back-up, but it's money well-spent.