We were lucky enough on our recent move to know someone who was also moving within about a week of us. All of the boxes we had emptied were easily handed off for reuse right away:
If you are in a similar situation, we highly recommend coordinating shared use of moving boxes. It was so easy for us: we didn't even break down the cardboard boxes before we passed them on to our acquaintance.
If you don't know of another person moving at such an opportune time, give it a go seeking someone out. We're sure a simple ad touting "free moving boxes" on Craigslist or just spreading through word of mouth would receive a great response - especially at a time of year when a lot of people are relocating.
MORE ON MOVING BOX REUSE:
(Image: Hop Studios)
Small Cool Lessons: Discovering Small Space Design Ideas That Really Work
Marisa and Peter's Playfully Eclectic Home
Good Food to Share 
The Big Book of Small, Cool Spaces 
Apartment Therapy Presents 
The Eight-Step Home Cure 
Sheex Bedding
Eileen's Beachside Oasis Kitchen
How to Make Fresh Pasta Dough in the Food Processor
When we moved to the house we are currently in, there was another family moving out of a house right down the street. They came over and asked for your empty boxes. It worked out pretty nice for everybody!
I posted my first wave of boxes on Craigslist on Sunday. Ten responses in half an hour. Super nice guy picked them up an hour later.
Call me paranoid, but in NYC and Chicago, I would be very very concerned about bedbugs. Sigh...
Freecycle is another place to give away or find boxes.
I got 40 slightly used boxes yesterday from a nice girl on Craigslist for $20. Totally worth it.
i *always* pay 'em forward and ask for a scout's honor promise from the recipient that they will, too!
U-Haul usually has a "used box" pile too - if I remember the rest, I'll post 'em later.
I've given away boxes everytime I've moved- mostly through Craig's List. Saved me a ton of effort and made me feel better that generally new boxes were being used again.
If you are moving, you MUST register for freecycle. Not only will it be super easy to find moving materials, not just boxes, but peanuts, packing tape and bubble wrap, it is also an excellent place to find furniture that people don't want to take to a new place. Or, you can give away things that YOU aren't interested in hauling to the new place.
You know, I love the idea of Freecycle, but I've had mixed results with it. Yes, if you need stuff, definitely sign up (especially if you have kids, because they're always giving away tons of kid stuff). However, I've had lots of problems with people not showing up when they say they will. I get boxes at work and I go to all this trouble to flatten them, haul them home in my little car, store them in my tiny garage, then post them when I have a stack to give away. What happens is that at least half the time, the people who say they want them don't show. I felt like I was doing the right thing but I had to stop doing it because of the hassle involved. I'm sure some Freecycle groups are better than others on this issue, but it's a real problem here.
My parents and I have been doing this forever. After each move, the boxes get broken down and whoever has the space to store them (even if it's just cramming them under a bed or in the back of a closet) stores them until whomever moves next. Usually a box or two will get damaged in a move so it's likely whoever is moving next will have to find/buy a couple extra boxes, but it does help out. It's must better than trashing them.
Last time I moved I put my pile of boxes outside in the alley. I put an ad on craiglist saying they were there, and that I will not hold them for anyone or answer any emails. Within a couple hours i had like 10 emails ranging from people asking if i would hold them to people asking if i had any boxes of a specific size. No one picked them up so I recycled them a couple days later. Frustrating.