A friend of mine has a fat, spoiled, indolent Siamese cat, and I put on an effete, supercilious accent of an ivy-league snob for it. "You silly girl, why don't you feed me the beluga caviar the way the Vanderbilts did?
I don't have pets. But I do a specific voice for babies. It's like some odd deep street eastern European / Russian type thing for some reason. And I normally say stuff like "Ay! You! Wha-tis you doin', yo?"