When I had room for them, I kept all the boxes. When I was running out of room, I kept one for each type of speaker. When I didn't have the room any more, I threw the boxes away. When I moved across the country, I lamented getting rid of the boxes.
The movers were great, though, and everything arrived unharmed.
That's quite a parable.
Some people toss the styrofoam and keep the boxes but flatten them down. You can always find new bubble wrap later in future shipping but finding a good fit box is tougher, though Uhaul has a pretty good selection.
I keep all mine in the garage rafters.
