In Hyper Police, the main character Natsuki Sasahara is a cat girl who lives with several dozen cats. Likely subverted by the fact that she is half cat goddess; her mother is the Egyptian sun goddess Bastet.
As of 583 we have been further confused by the revelation that Komamura's grandfather is a a gigantic, non-anthropomorphic canine, who is apparently none-too-pleased at Komamura's former shame at hiding his appearance. We later learn that Komamura comes from a clan of werebeasts.
In The Cat Returns, ordinary housecats are extremely spooked and agitated at the arrival of a parade from the Cat Kingdom, containing cats that, aside from walking on two legs and holding things, look exactly like normal cats. This is made funny when anthropomorphic tuxedo cats, bouncers, stomp around and bully the riffraff away.
One episode of Kirby of the Stars involved a colony of evil penguins on a motorized ice floe taking over Dream Land after their own home was destroyed. Wait a minute, isn't King Dedede also a penguin?note It should be noted that those same penguins appear as enemies in some of the Kirby games as it is. Though Escargo(o)n does call the Wandering Pengi "Your Majesty's relatives", at least in Japanese.
The anime frequently features non-sentient fish. One recurring character, Kine, is a talking fish. A late episode has a slightly disturbing scene where Kine tries talking to some of the main characters while they're fishing. He doesn't seem to understand why this is a bad time for a chat. Then they explain that he could end up as sushi if he sticks around, and he's naturally terrified. On that note, the episode in which Kine was introduced*
included a scene where Chef Kawasaki tried to cook him and feed him to a customer.
In Naruto, there are talking dogs like Pakkun and non-talking dogs like Akamaru. The strange thing is that both seem to be of about the same intelligence (Akamaru can actually use Jutsu) but only one can speak the human tongue. Possibly justified in that Pakkun is a summoned animal (who all seem to talk, being mystical creatures and all) while Akamaru is just a normal dog. Well, normal aside from the fact that he's trained in ninjutsu.
One omake has Naruto lampshade Pakkun speaking (who apparently was taught by Kakashi to do so) to Kiba (who can understand Akamaru's barks). The latter confirms that Akamaru will eventually be able to speak human like the other dogs in his clan, but whether it comes naturally or with outside aid is left ambiguous. Akamaru then tries to speak to Naruto. His first words; Meow.
It has been thoroughly pointed-out that the animal-characters on Nagasarete Airantou look nothing like the animals everywhere else in the world. Meimei makes costumes of the said real animals, drawn rather realistically for effect, that scare animal-characters of purportedly the same species.
In Eden's Bowy, Ms. Nyako, a humanoid catwoman, is absolutely shocked to hear a talking white leopard (secretly the goddess Enefea, who had been punished by her father, the god Lumezavia, to be trapped in such a form.)
Ms. Nyako: What?! The cat spoke?!
Very easily Hand Waved due to the nature of One Piece. This is slightly averted for all Zoan type Devil Fruit users, who are animal-humans, but is played fairly straight with Tony Tony Chopper the human-reindeer.
Some creatures are still of very questionable species, however, seeming to be neither human nor animal and yet not stated as Zoan-types either, such as Hamburg from the Foxy Pirates, who seems to be a Gorilla-man but is otherwise not shown to be a zoan-type user.
Being that the Digital World and Real World are entirely separate entities, this is inevitable in pretty much every Digimon canon, with both animals and animal-inspired Digimon sort of coexisting. One of the best examples comes from Digimon Adventure, where Kari has both an actual pet cat, Meeko, and is partnered with Gatomon, a cat Digimon; the two don't appear to ever meet though. Also, while fish-based Digimon do exist, Gomamon's Marching Fishes attack appears to summon real fish, even in the Digital World.