Fantastic Mr. Fox
The mammals in the movie are anthropomorphic, the other ones aren't. Mr. Fox kills several chicken to eat them. The results are sometimes shown. An anthropomorphic rat character dies after a fight. Despite him being a villain, the scene is emotional but not brutal. Mr. Fox has his tail shot off. He doesn't seem to be in pain, but is rather angry and hurt in his pride. Later, the tail is ripped to pieces by a dog, Mr. Fox gets it back, poorly glued it together and attached it to his backside again. During much of the movie, the entire society of anthropomorphic animals is in peril, but all of them survive.
We also get to learn that the animals, despite being anthropomorphic, only live as long as their real life counterparts.
Far from the Madding Crowd
A herd of sheep are rounded up by a sheep dog and he chases them off a cliff. They all die. The farmer is so upset and shoots the sheep dog.
Linford the dog is seen in a few scenes and comes to no harm.
Uh...well, a demon snake is pulled out of a woman's belly and then swallowed whole by a man. Does it die? Does it turn into the monster that later appears? Since it was a demon, was it even alive to begin with? No clue. The only reason it's worth mentioning is because the demon snake is played by a real-life, six-foot-plus albino Burmese python.
A dog is killed. The death takes place off screen but afterward the dog's head is shoved through a doggy door to frighten the family.
Animated. Cats are killed, experimented on and electrocuted. A dream sequence features disemboweled cat corpses used as puppets.
When Dory arrives at the quarantine, the other fish think that her parents died, but in the end of the movie, it is shown that they are alive.
Finding Rin Tin Tin
No dogs are harmed or die. A dog and her three puppies survive the bombing of a town unharmed. Rin Tin Tin is one of those puppies; he makes it through the film without being hurt.
Three tracking dogs are killed off screen (we hear their yelps). A wild pig is killed with a spear off screen; we see its butchered leg. A number of rats attack a man and he throws them off of him.
Flowers in the Attic (1987)
Fred the mouse dies after eating a poisoned cookie. Several German Shepherd guard dogs appear but none are hurt.
The titular Fluke finds himself in various threatening situations but does not die. Another dog is shot and dies while helping Fluke escape from a cosmetics lab.
A dog is shot and killed during an air raid. His realistic-looking body (best case scenario, it was a live dog that was drugged for the scene) is carried around for a while and then buried. Other animal corpses are seen and buried.
Dog are seen and heard in a few scenes but nothing much happens to them. A number of horses fall down in battle scenes but none seem hurt; most of them immediately get up and run off.
Two guard dogs attack the main character. They aren't hurt.