Many thanks to Machiko, who wrote to tell me about the fascinating practice of Ningyo Kuyo in a Japan. She says, "I read your article on clearing Teddy Bears with great interest.  I am not sure if my tip will help people living outside of Japan, but a lot of temples hold ceremonies there to thank and part with worn-out dolls and teddy bears."

She says this is a ceremony offered at many Buddhist temples and Shinto shrines. People bring (or in some cases, mail) dolls and teddy bears they no longer use, and for a small fee (around ¥ 3,000-5,000) a ceremony is performed.

In Buddhist temples the ceremony consists of a sutra being recited for the dolls or bears, followed by a ritual purification called Otakiage (burning in fire). In the Shinto tradition, the ceremony begins with Mitama Nuki to remove the Mitama (soul or spirit) from the dolls or bears, then there is then a prayer for the owners, and finally there is an Otakiage purification with fire.

Machiko says, "I have not been able to find the origin for this specific practice, but the practice of holding a ceremony or building a monument for everyday objects such as sewing needles and pens/ink brushes to thank them for their services has been historically done (it may have originally come from China), so I believe that it is natural for the Japanese people to hold such ceremonies also for dolls." She says similar ceremonies are also done for letters that for some reason could not reach their intended recipients.

More information I've found about Ningyo Kuyo:
http://www.tricycle.com/blog/jeff_wilson/3554-1.html

Photos of ceremonies:
http://www.geocities.jp/kiyomizudo/ningyo2.html
http://ningyou.org/article/26754730.html

Machiko says, "In my case, when I cleared my old teddy bears I simply thanked them and took them out as regular trash.  It was my simplified version of the ceremony, and I believe that it is more environmentally friendly. Although many of your readers may not have the chance to use the services offered in Japan, I believe that certain forms of ceremony, such as offering flowers, incense, food you used to enjoy with teddy bears as a child, and thank-you cards (the cards may go with the teddy bears or stay with you), may help them with clutter clearing teddy bears."