I've always thought of Polonius as being like a fox—smart, cunning, kind of cuddly in a funny way. (Yes, really).
Gertrude is a mother hen, forever moving about and clucking, making lots of noise, and quite annoying after a while.
Ophelia—poor, sweet, delicate Ophelia—is like a little swallow, ever so charming as she delightfully flutters around, but really too gentle, too fragile for this harsh, unforgiving world.
Claudius can only be one animal, really: a snake, a poisonous, cold-blooded serpent slithering its way into the Edenic paradise of Denmark under the reign of King Hamlet and spreading moral corruption everywhere.
Rosencrantz and Guildenstern always remind me of a couple of puppies: playful, fun to spend time with, but also easy to control and not very bright.
Laertes is the proverbial bull in a china shop, brave and strong, and forever barging into a situation without thinking about it.
Horatio is a two-legged version of a four-legged friend: a horse. In the words of the song: "He'll never let you down / He's honest and faithful right up to the end." Sounds just like Horatio.
And then finally, what of Hamlet himself? He's a strange creature, Hamlet; he's almost like a hybrid. When it comes to making a move, he's like a sloth; in his treatment of Ophelia, he's a real snake; in devising the elaborate plan to expose Claudius, he's like the proverbial wise owl; and when he ensures that Rosencrantz and Guildenstern are killed in his stead, he really does resemble a weasel.