Walk into moving and storage supply stores, and you'll see giant rolls of shrink wrap near the bubble wrap and tape. You may wonder if using that shrink wrap on your furniture and possibly your boxes is a good idea before putting them on a moving truck. The plastic, it stands to reason, could offer more protection against spills, rain, and other moisture problems. But it's also a generator of more waste. When is it appropriate to add that shrink wrap?
When There Is Rain
If you're planning to move on a day when heavy rain is in the forecast, and you know the boxes will get very wet on the way to and from the moving truck, plastic wrap could be very helpful. Light rain can get the box wet, but it generally won't be plentiful enough to really soak through the cardboard and get the items inside wet. If you're unpacking quickly and getting rid of the boxes, light rain isn't enough to warrant plastic shrink wrap. But heavy rain could soak the box, make the cardboard weaker, and increase mold risk if you think unpacking will take a while.
Moving Into Storage
If you're moving items directly from your old place to a storage unit, then yes, you'll want to wrap everything in plastic. The plastic protects the boxes from most pest intrusions and also from spills that occur in your or neighboring units. The plastic also makes it easier to wipe dust off the boxes, which is important if your storage unit is an "exterior" unit, where the door leads outside, rather than into a hallway.
Any item that has loose parts or parts that could potentially catch on clothing, such as a bookcase you've disassembled, should be wrapped up. Use either the shrink wrap or a very large plastic garbage bag. The plastic simply helps contain those parts into a nice package.
Shrink wrap can be hard to use by one person who isn't used to using it, so you can always ask the moving company to add it. That may add packing costs to your moving bill, but the costs shouldn't be as extensive as those for full packing. And those costs may be worth it to protect your belongings from pests and moisture problems. After all, it's cheaper to wrap everything in plastic than it is to spend time and money replacing items that have been damaged.