I have a tendency (or possibly obsession) to keep packaging for items that are open. I would suggest definitely keeping all packaging for statues, busts and the like not only for the art but in case you do move. Remember how it went in the package might be tough after a while, but when we moved last (10 years ago) putting statues back in their package ensured they arrived in great shape.

For figures (even 1/6 scale) I would suggest maybe removing the inserts and then folding the boxes to keep them but reduce their size. They can be stores under a bed or in an attic or basement. Moving you will be better off putting the figures in bags and then in other boxes than trying to re-package them. The figures will survive just fine this way.

-Rob

Sometimes the packaging is pretty cool. Those Masterpiece Transformers boxes from Takara start to look really nice together.
But then I moved house, and everything went bye bye. But now i find myself doing it again, and keeping boxes. Empty boxes!! Why do I do that?

For decades my adage was, I collect action figures, not blister cards.

I gleefully open all my toys first thing and pitch the packaging almost immediately. I simply don't have room, to archive even flattened boxes.

Yes, tho$e inSanely cool Mythic Legions figures by the Four Horsemen have incredible collector friendly, easy-open bubble cards, but even though they can provide handy storage for myriad accessories, the packaging takes up far more room that the accessories themselves. I usually store worthwhile accessories (not displayed with one figure or another on my shelves) in small ziplock bags in my "parts drawer." I've often wished that more figures came with stands that contained their own small "parts drawer" for such storage.

However, I have made some exceptions. For certain Asian toys I do try to hang on to the packaging. I recently bought both of those large Voltron figures and the boxes were just too nice (although large) to throw away.

I keep all my boxes. While it adds to the shipping costs when reselling, it usually more than makes up for it with the added value to having the box.