A dog called The Beast (aka Hercules) is injured when a fence falls on him but he is rescued and recovers. At the end of the film we find out he lived to be 199 in dog years.
A cat and a dog appear throughout the film. The cat gets in a fight with another cat off-screen but is not harmed. Though there is talk about putting the dog to sleep because of bad hips, the dog is alive and well at the end of the film.
Chris, the family dog, survives a massacre and fire unharmed. A rock is thrown at a barking dog. On the livestock front, dead cattle and horses are seen. John Wayne shoots at a herd of bison but we only see one fall down.
The Secret Life of Pets
Animated. While the group of pets that are the heroes of the story are often in peril and there are moments where it looks like they might not survive, they all make it through unharmed. There is one animal death in the film: a "bad guy" snake is crushed to death under a pile of rubble after trying to bite the main characters.
The Secret of NIMH
Animated. Three main characters who are rats die: Nicodemus (a good guy), Jenner (a bad guy) and Sullivan (a reformed bad guy). Mrs. Brisby the mouse, her family and the rest of the main characters do not die, though Mrs. Brisby's husband is dead before the beginning of the film. Dragon the cat does not die.
The Shaggy Dog (2006)
Animals are experimented on and suffer some slapstick accidents (a dog runs into a window, for example) but no pets are seriously hurt or die.
The Shawshank Redemption
Brooks' pet crow, Jake, is freed and does not die. This is different from what happens in the original short story, where Jake is a pigeon instead of a crow and he turns up dead shortly after being freed.
The Silence of the Lambs
Despite the title, no lambs are seen in the film (unless you count lamb chops). We are told that The dog Precious survives being knocked into an empty well but we are told she has a broken leg. Two cats appear briefly; Catherine Martin's cat, who she calls Little Cheeper and an unnamed cat in the home of Fredrica Bimmel. Neither are harmed.
The Skeleton Twins
After being purchased, two goldfish are forgotten in a bag and die. After a day, they are discovered and are put in an aquarium in an attempt to revive them but it is too late.
The Son of No One
The dog Charlie bites a bad guy and is then kicked/stomped by the bad guy. The bad guy is killed but Charlie still dies shortly afterward.
A kitten named Muffin is fed a bad serum and melts, leaving only her eyeballs.
The Starving Games
The main character is about to shoot a deer with an arrow for food but is interrupted and accidentally shoots a man instead.
A girl asks if she can eat the main character's pet hamster and holds up its cage with the scared hamster inside, but she gets no answer and we never get back to this topic. The soul keepers from Avatar are killed with a fly swatter and through electricity, but they look more like flowers than animals.
On a big screen a poorly animated cartoon unicorn is impaled, but you can't really count that.
In the outtakes, an actor jokes that a cake is made from fox blood.
The Stranger (2014)
A dog is attacked and shown with very bad injuries. He's still alive when you last see him but survival doesn't look possible. A cat and rat also die and is shown.
The Thing (1982)
An alien life form appears as a dog and grotesquely absorbs the other dogs in the kennel into itself.
The Three Lives of Thomasina
Thomasina the cat appears to die but is brought back to life. A sick and elderly dog (Rabbie) is left at the vet to be euthanized and later we are told that he was put down. Bruce, a guide dog, is hit by a car but saved by a veterinarian. Other animals are injured (a frog, a badger) but are healed. In a circus that is eventually shut down for animal cruelty, horses are whipped offscreen and an injured bear is forced to dance.