Despite the fact that animals can walk and talk in Shirokuma Cafe and are apart of human society, fish appear to be an exception and are eaten freely. Interestingly, cows, pigs, and chickens appear to receive the same treatment, as there are still hamburger restaurants, and in the manga at least one character cooks a roast chicken. The issue is mostly ignored, but it doesn't appear to be wholly illegal for animals to eat other sentient animals.
Kimba the White Lion has played a bit with this problem (despite being guilty of this trope itself in early episodes): after all animals make peace under the new "lion king", they are suddenly facing a situation where no-one is allowed to eat anyone else, thus reducing their entire carnivore population to live solely on insect (and THAT gives them moral qualms; lucky that a man who's been trying to invent "artificial meat" eventually comes along...)
Pokémon seems confused on whether all animals are Pokémon, and whether Pokémon are both intelligent and edible:
The cast eats meat on several occasions. Whether the meat is from Pokémon or regular animals is never stated (though see below).
When Ash caught his Krabby he was worried Oak was going to eat it. Professor Oak dismissed him because it was too scrawny to make a good meal, and said Gary's much larger Krabby is more appealing.
In one episode the heroes and Team Rocket are starving on a makeshift raft in the middle of the ocean. Everyone wants a taste of James' juicy Magikarp, except Misty who has a soft spot for Water-types. The only reason Magikarp survived was because its scales were too hard to bite through.
Pikachu and Pichu are shown to have teeth more like cats than rodents, canines and all. Still they're only shown to eat berries and other herbivore-safe foods.
The games are much more explicit on the matter; predation does happen, and Pokemon do eat other Pokemon. For example, Durant is eaten by Heatmor (as they are an ant and an anteater respectively), Yungoos and Furret both hunt Rattata, and Omastar preyed on Shellder. Less frequent, though still present, is mention of humans eating Pokemon. Farfetch'd is stated to be endangered because it is a popular dish served with leeks, and Basculin is also said to be "quite tasty".
Arashi no Yoru ni (One Stormy Night) is a heartwarming movie about a clumsy, mangy wolf named Gabu making friends with a sweet (if somewhat androgynous) goat named Mei. The wolf repeatedly had to suppress the urge to eat him and his kind, which his goat friend is blissfully unaware off (unlike his more wise nervous friends). For example, while going out on a picnic, Gabu loses his meal and (delirious with hunger) thinks about gnawing off Mei's ear under the assumption that friends should make others happy.
Even more heartbreakingly, At one point, the two get stuck in the snow together. There is no grass around, so Mei will almost certainly not make it back home alive. There is no prey for Gabu to eat, either...except Mei, that is. Gabu refuses to listen at first, but when Mei points out that he might be able to live if he eats him, and that Mei will almost certainly die anyway, he reluctantly sees things his way, though not at all happily (and almost immediately changes his mind). Luckily, they find a way out without having to resort to that. Honestly, the whole movie could be seen as a deconstruction / reconstruction of the trope.
Yume No Crayon Oukoku has an odd situation. The Crayon Kingdom has several neighboring kingdoms, such as the Hamburger Kingdom and the Rice Ball Kingdom. When dignitaries from all these kingdoms were invited to a banquet, we couldn't help wondering, "What do the hamburgers eat?" The question was answered: they eat smaller, non-sentient hamburgers.
Averted in Wolf's Rain, where in spite of the wolves' ability to replenish energy by sleeping in the moonlight, it's clearly no substitute for actual food. Kiba mentions having gone a month with only moonlight to sustain him, and consequently is much thinner than the others. They find a decomposing deer carcass in one of the early episodes (which everyone but Hige turns down, generally because it's rotting). After Toboe's Crowning Moment of Awesome where he kills the giant walrus, they eat the walrus—and in a surprisingly dignified acknowledgment, the walrus says something along the lines of, "You may have killed me, but I have saved you all."
This bit of dialogue between Goku and Oolong (Who is an anthropormorphic pig) in Dragon Ball:
Goku: Do you like bacon?
Oolong: WHAT ARE YOU, BRAIN-DEAD!?
In My Bride Is a Mermaid, a good portion of the primary cast are mermaids, and as a result the question of whether or not eating non-sentient fish counts as cannibalism comes up more than once. It's almost always played for laughs:
At one point, a character introduces himself and begs the onlookers not to overfish him. Later, when he's offered sushi, he identifies the fish as "the guy who taught me how to ride a motorcycle". Said fish then gets a full flashback treatment. The fact that many types of fish naturally eat other fish is never mentioned.
A Human/Mermaid version comes up early in the show: the merpeople have taken over Nagasumi's school (don't ask), and one of them, Nakajima, an octopus mermaid who's only ever seen in his octopus form and is almost always missing a few tentacles, teaches the home economics class. Teaching the students how to cook octopus. With what's heavily implied to be his own severed tentacles. Nagasumi passes on eating the result, just in case.
In Sayuri Tatsuyama's Happy Happy Clover, all of the animals (Especially Rabbits and Squirrels) in Crescent Forest live in some form of harmony with each other, and predators like foxes and owls don't seem to eat meat. Heck one of the main characters is an owl named Professor Hoot who the Forest's teacher and doctor. While Cinnamon The Fox and Twirl The Squirrel can sometimes get along with each other but mostly cause arguments with one another.
Non-sentient fish are regularly seen on Kirby of the Stars, usually as food. Kine, meanwhile, is a talking fish. In one late episode, he tries talking to the main characters while they're fishing. They explain why this is a bad time; namely, that if he sticks around he's likely to be made into sushi. Upon hearing this answer, he's understandably horrified. Also note that one of the characters giving this explanation went on a date with him at one point.
Kine: Can't love work out between different species?
Fumu: The problem here is that we also see each other as food.
During the episode where said date took place, Chef Kawasaki tried to cook Kine and feed him to a customer.
Escargo(o)n has been shown on various occasions to be less than happy about the fact that some people eat molluscs, including snails. Nobody else seems to have a problem with the idea, despite the existence of snail-people. At one point, Dedede even offers Escargon some of the shellfish that he's eating - Escargon refuses for obvious reasons.
Chef Kawasaki (listing some of his "unique" sushi creations): ...And snail sushi!
Escargon: Are you trying to make me a cannibal?!
Actually a major plot point in Animal Land, where one of the goals of the protagonist who can understand the cries of all the animals is to get all the animals to understand each other and cultivate a meat-substitute plant so that the predators can survive without eating other animals. In the meantime, the predators living in the village with a bunch of different species he brought together stick to eating fish, although the protagonist has been warned that eventually he'll start to hear their voices too.