Static Safe
Ground yourself before you touch anything inside a computer case. You can do this easily by just touching the metal power supply case while it is still plugged in.  Dry winter months are when you have to be especially careful because just walking across a carpet you can build up enough static electricity to not only shock yourself but pretty much destroy any computer component you touch.

Transporting Computer Components
If you have to ship or transport any computer component such as a hard drive or video card then you have to package it correctly to ensure it is not damaged in transit.  Any component should be placed in a Static Shielding Bag before it is carried or transported in any manner.  An ESD bag, Anti Static bag, or Conductive Grid bag are those plastic bags you probably have seen whenever you purchased a new component. They can be dark grey, grid pattern, bubble wrap, and even pink but each should be marked as a static shield bag.  I always save the ones I get from hard drives and other components because they come in very handy.  If you don't have any you can always ask your local computer store for a couple, when I had my shop I was glad to hand them out because they piled up quickly.  The ESD bag protects the component inside from static shock by shielding it while handled in an unsafe environment.

Hard Drives
Hard drives require a little more care in handling especially when shipping.  You have to remember that a hard drive is somewhat delicate in that it can be damaged by a sudden shock such as a drop or fall.  If you are planning on returning a hard drive to a manufacturer for replacement you need to follow their shipping instructions to the letter.  In most all cases you are required to ship the hard drive in an approved box and padding material.  A local computer shop may be able to help you with this as they normally save the boxes just for this purpose.  If you cannot not get access to the correct box you can usually request one from the manufacturer. 
Bench Tech Tip - If you ship a hard drive in an unapproved box the manufacturer can and will in some instances void the warranty