"Dead" hard drives can be resurrected long enough to extract their data. For instance, techs at my Day Job have been able to pull an amazing amount of data off "dead" but spinnable hard drives with GetDataBack from Runtime Software (www.runtime.org) -- these were from drives that Windows initially couldn't read at all.
And you might have seen advertisements for expensive data recovery services -- for $1000 or so they'll retrieve crucial data from cooked drives. What these data recovery services sometimes do is open up the dead drive in a clean room, take out the drive platter and install it in a new hard drive housing. Determined data thieves can manage the same thing.
So, if you have a "dead" hard drive, or a floppy, Zip disk, CD, etc. that you plan to chuck* and the device contains sensitive data you couldn't properly delete first, your best course of action is to mechanically destroy the device before you get rid of it. If it's a drive, hit the sucker with a hammer. Alternately, drilling a couple of holes straight through the drive works, too (but don't try this if you don't have the proper drill or safety gear). If it's a CD or DVD, find a CD shredder, or break it up with a hammer. I've been able to recover data from CDs that were broken cleanly in half, and I've seen other techs recover data from floppies that have been folded in half. So, chop 'em up. I don't recommend incineration because the plastics and metals used in the devices can give off poisonous smoke and leave behind toxic ash.
* When getting rid of a bad hard drive, it's best to call your recycling company to find out where to properly dispose of it, since hard drives may contain toxic materials.