I have all of mine (at least those that had boxes when I bought them). Sure makes it easier to move when you know the models are secure. Every time I have moved, I have spent days returning my models to their original boxes, and then packing them, myself, into larger boxes. Then I follow each one of the boxes out to the moving van and make sure they do not stack heavy stuff on top of them.
At the very beginning I don't think I kept them, when I was first collecting if a box had a nice pic of the car on it i would cut out the pic and put it on my wall among many other pics of cars, but now I keep everything with the boxes including screws (which has really payed off as I have had to repackage them twice because we moved)