try annthegran click on download designs up the top it will take you to a page click on agree another page will load where you can type in your request in the search bar, click search and there are heaps to choose from hope you find what you are looking for.

You have 4 free bears here (bottom of the page)

Dixie, if you mean a 3 dimentional bear insted of a embroidered design, try www.moosbestitin.com and have a look at the hugums, there is an adorable bear with blankie. I bought the design myself and it comes out great. I sewed it out on some beige stretch velvety fabric I bought from lincraft at only $6.99/mtr it worked a treat and because it is 140cms wide you can get about 20 bears out of each metre! Hope that helps cheers, Ruth

and another one here

on these sites they have a new free design every 10 minutes, very often there are bears too. the designs are mostly in small format.

On SewForum there are bear dolls in 3x3 and 5x7 that are made in-the-hoop. Log in and search for "bear doll" in free embroidery designs. The author is perfect_fit. There are also cat, dog, bunny, and cow dolls available.
http://www.sewforum.com/

There's a small in the hoop pattern at joydesign, have a look. It's a free pattern meant to sew for their charity. Maybe you can ask permission to use it for yours.

Dixie, one of the CUTE members has a free one - you can go to this project and get the info on it and view the bears, too!