You’ll never waste more boxes in your life than when you move. I recently moved and posted an ad in the free section of my local craigslist for the leftover boxes and got many responses. This free bulletin board exists in most US cities, and I advise you to do the same.
If you have 20 or more reusable broken down boxes, another option is to contact Used Cardboard Boxes. They will pick them up for $4.95 (proceeds go to plant trees) and will sell them/rent them to other people.
Consider using Used Cardboard Boxes for your next move, and then you won’t have to worry about getting rid of the boxes — they just take ’em right back. You can also rent plastic bins in many places.
Moving Box Exchanges are popping up all over!