I need to remove one of my hard drives, and it will stay outside of any computer for about one month. I've got a lot of sensitive data on it, so I want it to be safe and healthy.
In what should I keep it in order to not damage it? I don't have the plastic box it came with when I bought it, so in what else can I store it so it will stay safe?
You certainly need an anti-static bag - if only to keep the dust out!
If you can find somewhere stable to store it - such as a shelf - where you're not going to have to move it again until you put it back into your computer, you should be able to get away without the padding. You only really need the padding if the drive is likely to get bumped.
Basically don't keep moving it.
The Journeyman geek is right, store in an anti static bag and then inside a padded container. However, I would add a bag of Silica Gel (the little white bag you get in most boxes of electrical goods) to absorb any atmospheric moisture.
Keep the hard drive in an area not subject to big temperature changes (which may cause condensation).
anti static bag, then some padding (in case)- our local small hardware stores sell em in plain old anti static bags.