According to Umbra from grist.org:
If you wish to recycle the plastic cases, it might be a bit tough. These are #6 plastic (polystyrene), which may be recyclable where you live — be sure to check with your local authorities. Since #6 is not wildly popular, a better bet might be one of several outfits around your country that will recycle these items for you; generally your costs are just for shipping. Check out GreenDisk, which takes all manner of “technotrash,” from iPods to X-rays; CD Recycling Center of America, which has several locations around the country; and CD Recycling Central based in California, which recycles other e-waste items too.
What happens to your CD cases when you send them off this way? According to Earth 911, they are simply recycled into new plastic items, which we hope will be useful to someone — and then eventually recycled again.
You could also contact your local library to ask whether they need any replacement cases — I see from many discussions online that library patrons are wild and reckless, and CD cases often come back smashed. Many people also recommend posting the cases on a site such as Craigslist or Freecycle. One man’s trash, and all that.
Other option is to reuse/repurpose/upcycle them, here some ideas: