Hard disk wiping - single vs multi-pass

I worked in a decom department for a while, wiping hard drives... but I never knew the difference between a single pass wipe, or a 3 or 7 pass one. I know the disk is written multiple times to ensure that all the data is gone, but what's the point in more than one pass? Surely if a drive has been completely written with 00's, nothing is recoverable... what are the benefits of doing this multiple times?

Multiple passes weaken the "residue" until eventually it's virtually indecipherable.

Technically, you can't ever completely wipe a disk. Old data tends to slowly bleed into the area between tracks, so even if you wipe several dozen times, the new data hasn't been there long enough to wipe what's between tracks. So long as you don't wait too long, the old data is still accessible by some (amazingly expensive) lab techniques.

The only way to guarantee unreadability is to destroy the disks. For higher levels of classification, DoD resorts to pulverizing and melting old disks.

I know that's what >>2 meant by "virtually", but I just wanted to clarify for any readers. As long as the disk exists, someone can read old data off it. The question is whether it's worth it for them to do so.