•Hercules trained Pegasus to "sit" in the Disney animated movie.
In The Hunchback of Notre Dame, Phoebus has taught his horse Achilles to sit. And heel. Horses can be trained to sit as depicted in the film, although it's extremely tricky, requires a good trainer and usually doesn't involve a verbal command.
Despite research with real animals and attempts to avoid it in The Lion King, it happens when Scar brings out a zebra leg for the hyenas. They promptly sat up and begged with their tongues hanging out like dogs. There's a bit of Fridge Brilliance when you realize it's to show he's domesticated them with Magnificent Bastardry. Hyenas are technically distant cousins of dogs, but so distant they're also halfway to being cats.
•Atlantis: Milo's Return featured a lava whale that acted like a puppy.
•Played straight and to the extreme in WALL•E, where a cockroach behaves like a dog... and somehow manages to be cute, too.
In A Bug's Life, the queen ant has a pet aphid who acts just like a small dog. There's also Thumper the attack grasshopper who acts like an angry guard dog.
How to Train Your Dragon. The titular dragon has behaviors borrowed from cats, dogs, horses, and even wombats. Each dragon species has a mix of different animal behaviors. Terrible Terrors purr like cats and vocalize like chihuahuas. Nadders have mostly parrot-like traits, though Stormfly enjoys a good game of fetch. Whether the scratching neck = fall asleep behavior is modelled on dogs or cats is up for debate. • Toothless does have some more obvious dog-like traits, though - in the short Gift of the Night Fury, his technique for convincing Hiccup to come for a flight is very similar to a dog telling its master it wants to go for a walk.
•In Toy Story 2, Bullseye the horse acts much more like a dog, wagging his tail, licking people, coming when called, and whimpering like a dog in the third movie. Which is strange, because the character that is actually a dog, Slinky, does NOT act like this, and Buster, who is a non-toy dog, does. So aside from not being able to tell who is what from appearance alone they play this trope straight, toys are either humans or dogs. • The Toy Story short Toy Story of Terror has Mr. Jones, an iguana that behaves like a dog. He wags his tail, pants, fetches, and eats out of a dog bowl with his name on it like a dog.
Cars has farm and construction equipment acting like cattle, miniature VW Beetles like insects, miniature aircraft as birds, toy cars as dogs/cats/rodents, and model trains as snakes.