I'm in the military so yes, I do move a lot and when I move it tends to be to other countries. I also do a lot of local moves from one house to another or to other dormatories.

I guess it depends on what type of moving your doing. If your going from country to country or even from one side of the US to the other I would break down the components and place them in their original packaging. I learned that lesson on my recent move from England to South Korea. I shipped my computer in the case box with all components still inside. On the way over to South Korea my shipping container was outside in freezing temperatures for weeks on end. With everything bolted down inside I don't think there was enough room for contraction of the components and it caused internal damage. I'm just guessing though because when I powered it up I had all kinds of hardware problems and with no obvious physical damage that's the only thing I could think of.

If you're just moving locally I would just place your tower with all hardware installed in the box your case came with. I've never had a problem doing that for my local moves. If your using a moving company or having friends store items I would remove your hard drives or SSD and keep them with you. On my first move from the states to Portugal my whole computer got stolen from my shipping crate. I lost all my pictures and music, so I keep everything with me to make sure that doesn't happen again. Computer components are resilient even if you move a lot. I wouldn't let moving keep you from building a computer.