usedcardboardboxes.com buys up massive lots of cardboard boxes that have been used once by other companies, and then packages and sells them as "moving kits" that are a convenient size for moving particular sizes of households (expressed as number of bedrooms). They are delivered flat in big flat boxes, with other supplies thrown in: generally packing tape, markers, packing paper, and box cutters.

In an effort to be a convenient "one stop shop" for moving supplies, they also sell new cardboard boxes for special purposes, such as wardrobe boxes and file boxes, as well as other moving supplies, like mattress covers and blankets. However, when I did some comparisons against my local U-Haul store, U-Haul had better prices for those things, and since the specialty boxes and other supplies are new in both cases, there's no added virtue for getting them from usedcardboardboxes.com.

The used boxes carry the logos of whoever used them first, often with labels, writing, or scraps of tape attached, but otherwise they are not far off of new quality. The X-Large boxes generally have to be folded in half, so they'll have been bent once in a place that doesn't line up with all the box's intended seams, but this isn't really a problem once the box has been assembled and taped.

I've used UCB for two one-bedroom apartment moves now, and can share these conclusions:

• Their n-bedroom kits are essentially n+1 "Basic Studio Kits", with a little more of the extras, and the resulting estimate of how many boxes are needed per bedroom is on the low side. That said, a lot of my extra needed volume comes from how many books I have. So if you are a person with "collections"--books, nerdy collectibles, a serious set of cookware, etc., then you will need a lot of extra boxes.
• For books in particular, you will probably want their "small" boxes, which don't come in n-bedroom kits.
• The packing paper they give you comes in slightly bigger sheets than U-Haul's; it's great. However, they don't include quite enough of it; I always needed more.
• U-Haul has a fancier selection of specialized boxes for glassware, etc.

As a bonus, I found that it was easy for me to hand Moving Kits off to another person after I was done with them. I could package them right back as I'd received them, and let people on Craigslist know that they'd be getting "the boxes in this set, without all the extras and with one move's worth of writing on them". This had the side effect of forcing me to empty out all the boxes before I could pass along any of them. If that restriction is too harsh for you, leaving out one shipping box and its contents usually just results in a kit for one bedroom smaller, so that's still easy.

They also have a "UCBZeroWaste" service, which you may be interested in if you run a company who could potentially supply these boxes to them, or generally want to reduce the amount of waste your company produces.