We use 3 primary methods of media destruction. Which method that is chosen will, of course, depend on any number of factors including; corporate policies regarding data handling, legal or regulatory requirements, corporate policies regarding equipment refresh/retirement, time constraints, physical condition of the device, etc.
This would include any number of methods by which we attempt to fiddle with the bits on disk. The most typical is some kind of N-pass overwrite. This has the advantage of leaving the drive intact for use later, can be done in any number of ways, and is relatively configurable. Whether you use DBAN on a desktop PC with 1 or 2 drives or something like an ImageMASSter with expansion sleds and work on 20 disks at a time. This method also works equally well on removable storage such as ZIP or floppy discs. It has already been discussed fairly well at How can I reliably erase all information on a hard drive? Since it sounds as if the disk in question is failing, then this is likely not a reliable option and moving on down to a physical destruction method may be required.
In the olden days when you had a room packed with tape there were few things better than a big honkin' degausser for making sure that you knew what left the room. As hard drives supplanted tape, their use simply got transferred to the new medium. The biggest advantage to using a degausser to take care of hard drives is speed. Just pass a box through the unit, ignore the jiggling in your fillings, and walk away with clean drives. The downside is the lack of ability to audit data destruction. As discussed in the Wikipedia article, once a hard drive is degaussed, the drive is mechanically unusable. As such, one cannot spot check the drive to ensure cleanliness. In theory the platters could be relocated to a new device and we cannot state, categorically, that the data will not be accessible.
This is without question my favorite. Not only because we demonstrate, without question, that the data is gone, but the process is very cathartic. I have been known to take an hour or so, dip into the "To Be Destroyed" bin, and manually disassemble drives. For modern hard drives all you need is a torx set and time (possibly pliers). While one will stock up on their magnet collection, this method of destruction is very time consuming. Many companies have developed equipment specifically for hard drive destruction en-masse. These range from large industrial shredders to single unit crushers such as this beauty from eDR. I have personally used that particular crusher, and highly recommend it to any Information Security professional who has had a bit of a rough day.