I buy very few boxes. I save the boxes from year to year, unless they are in bad shape. I just flatten them, and store them away. I have a large stockpile of boxes in various sizes. I also try to remember to ask for gift boxes when I purchase items. I do the same things with gift bags, so I have a stash of those. I used to save tissue paper too and flatten it and reuse it. But I've mostly given up on that.
Unfortunately, the printed boxes don't save me any time because, like Cathymac, I wrap them anyway.