Back in the 80s, I had, literally, BOXES full of floppy disks.
Then I used to have several 250 disk CD holders with backups. Then I used the same ones for DVD backups, but could store a lot more. I still use them, but mostly for video clips/etc that we want to watch on the tv.
Then hard drives got cheap enough - and reliable enough - to keep a couple of larger standard IDE internals around just to copy things off to, then store away until I did it again. That was a pain, but not as much as losing all my "stuff".
Then until about a year and a half ago it was two Maxtor OneTouch 300GB usb drives. (Always keep a mirror drive - always)
Then two 500GB externals.
Now it's two 2TB WD externals, usb,firewire,eSATA, one drive operates continuously as a network aware backup drive, the other I rsync the first one to once a week or so, and when not in use it is stored in the firesafe. Even with the amount of backup data I have - about a terabyte+/-, dating back to the mid-90s for the most part with some older stuff going back to before Win3.1, I probably won't have to upgrade for at least a couple years.
I'm waiting for multi-terabyte solid state storage to get cheap enough... which it will, eventually...
Still, however, I do some really important backups - like my financial stuff, email, pictures, etc - to DVD, and store those in my safety deposit box. Along with a hard drive containing the same data, which I upgrade every year or so (hard drives are CHEAP nowadays, near enough free it makes no difference).
Paranoid, me? *g* Hell, yes. I've lost entirely too many memories, and important work, over the last 25 or so years because of media failure. I did all the video/picture work for a good friend's funeral in '99, and lost it all, because I didn't back it up soon enough. Never. Frakking. Again.
The importance of multiple backups cannot ever be stressed enough; even for what seems unimportant at the time, because one never knows what one might want to look at years later.