One of the in-house forum pages on which some Blogjob bloggers hang out asks, "What do your pets say?" My immediate reaction was, "That's an old, old, probably pre-vaudeville comedy routine." Admittedly these jokes are very old, but I've not seen them all collected in one place before. Here are some reasonable conversations it's possible to have in English with a variety of animals.
With a dog: "How's the weather out there?"
Human: "Do you need anything out there in the doghouse?"
(In a variant form of this joke, a man asks for free food and drink in exchange for the talking dog's entertaining the crowd. The first member of the crowd asks about the weather, or the road. "Rough." The next one asks, "Who is the best ball player of all time?" Back then "ball player" referred to baseball only, so the dog says, "Ruth!" The owner says, "Bah, humbug! That dog's not talking! Out!" and the dog says, "So, you still say Ty Cobb?" This is sometimes known as the Original Shaggy Dog Story.)
With a cat: "Where have you been?"
Cat: "Prowlin' around."
You: "You're late, but I suppose you want dinner anyway?"
(In a more elaborate variation on this joke, somebody posted a video of a cat saying "no" and "ow," allegedly while listening to [your least favorite political speech or other news story here]. The cat was obviously unhappy, and some viewers complained that the video must have been produced by some form of cruelty to animals.)
With a kitten: "What's the cutest animal God ever made?"
You: "Would anybody like a treat?"
(Etc. etc. etc.)
With a horse: "In Congress, someone has seriously proposed legislation to the effect that...[Insert the wackiest bill you've seen this year]. What do you say?"
Horse: "Nay! He-he-he-he!"
You, pretending to be serious: "Well, you know, there is some possibility that..."
Kibitzing cow, tired of waiting to be fed: "BAH! BOO-OO-OO!"
(No, I don't try to read bills pending in the U.S. Congress, except when e-friends alert me to especially valuable or ridiculous ones.)
With an owl: "What do you think is so funny?"
Owl: "You! Oo-hoo-hoo-hoo-hoo!"
(In a related joke, you ask a heron what his name is, and he says "Frank"--but in the U.S. humans whose name is Frank don't say it that way, so that joke must be obsolete.)
With a crow: "And how's your daily foraging going today?"
Crow: "Car! Car! Car!"
(A more realistic version asks, "How do crows keep each other safe while foraging beside the highway?" and answers, "By warning each other, 'Car! Car!'" This is almost literally true. Crows do warn each other when large animals approach; different crows work out different "languages," and some crow communities are known to use different notes--all of which sound like "car" to humans--to identify different types of hazards. In her Wickedary Mary Daly quotes an old book, which I've not seen, whose author reports that local rabbits had learned to heed crows' warnings.)