I'm having a contest over on my Deb's Going Green blog for ideas on how to recycle something old into something new. Bev E. sent in this great idea:
"When sewing or have left over small bits of yarn, I throw them in a pillowcase. Fill half way, then sew up the hole. Instant pet bed. I make and donate to Humane Society, AND just made a bunch up for the Veternarians office, for animals to lie on softly after having surgery etc."
I really like the idea, if you don't have any old pillowecases, they're usually pretty cheap at your local thrift shop.
There's an organization called the Snuggles Project that works to bring comfort to homeless animals. You can find a shelter near you that accepts these kinds of donations on this list. Please check with your local shelter to see if this would be something they can use.