When in need of moving boxes. or in need or getting rid of them, I have always relied on Craigslist and Freecycle. Now there is another cool option called BoxCycle.
BoxCycle has really though about all aspects of the box use:
"Retailers receive daily shipments in boxes that they then spend time and money getting rid of. While many retailers are happy to provide used boxes to others, they don't have time to look for interested people and do not want to be distracted from their core business. Recyclers, moving companies, and box manufacturers accept pennies for recycling perfectly good boxes instead of much higher prices people are willing to pay because these sellers are not setup to deal directly with consumers. BoxCycle shields sellers from frequent communication, broken appointments, payment collection, and other issues that makes dealing with individual consumers difficult. At the same time, BoxCycle makes it easy for sellers to list their boxes and find buyers."
There are probably many retailers who have loads of boxes available. You simply type in your zip code and it shows you all the potential boxes in your area. Sellers pay a commission to BoxCycle.
(Personally, I hope I will not have to move anytime soon).