It depends on the method.

If I was carrying it on, I would probably not do anything other than back up the drive first.

If I was not carrying it on and it was going to be shipped, I would back up the drive first. I would probably pack the inside of the case in the big bubble warp just to keep things from moving around, and if something did work loose it would not be bouncing around inside. Depending on the machine, if it has a optical drive that has a tray that opens for example, I would put some painters tape over that to keep it closed (think of all those irritating bits of tape you had to pull off when you got it), and I would leave a disk in the drive. If the drives are hot swap easily pulled out I would make sure those are secure too.

I would double box it, preferably in a computer shipping box, pack the tower, put that in a box, and then put that box into another box.

Either the computer or the inside box would go inside a plastic bag to prevent water damage should it be out in the pouring rain being put into the plane.

Name and address on the case, in the case, and on each box.

If I was checking it with the airline, I would say good bye to it, because I feel my chances of every seeing it again would be very slim.

If I was shipping it I would insure it for it's full value.