I have a dog who "plays" with fabric. Fabric for sewing or storebought blankets. Either way, he loves fabric. I'm careful not to leave pins in fabric. He also loves pillows and upholstery.
My cat's a gentleman... Unless you've hung a poster up on a wall, he'll grab the top and surf all the way down through the poster leaving it in two pieces. Although it looks like a lot of fun, I no longer hang unframed prints. :0D
Edit: sewjoyce, my poster surfer is a Siamese.