According to Herodotus, in his Histories:

"In households where a cat dies a natural death, all the people living there shave off their eyebrows -- nothing more. In households where a dog dies, they shave their whole bodies, head and all."
Oxford World's Classics (1998), trans. R. Waterfield. p. 121

I had no idea. Ancient Egypt has such a stereotype of cat-worship, but I realize I've never known a thing about the status of dogs there and then.