The cat General is tortured with electric shocks, wounded by a tiny monster, and threatened with euthanasia but ultimately lives. However, a pet parakeet is killed by the tiny monster.
Charlotte's Web (2006)
Wilbur the pig, who is at risk of being slaughtered for dinner, does not die. Charlotte, the spider who rescues him, does die.
Many wild dogs appear and attack people but we don't see any of the dogs die. The desiccated corpse of an animal is briefly seen; it could be a dog but it's hard to tell.
This animated films centers around a chicken farm filled with anthropomorphic poultry, and the threat of being killed and eaten is prevalent throughout. In the first scene, a hen gets beheaded just off-screen for not laying eggs. There is a dramatic bait-and-switch moment where it looks like a character got beheaded, but is revealed a second later to have dodged the ax.
Children of Men
Many animals including cats and dogs appear in the film. Most of them don't die, but in one scene it is implied that a dog is poisoned off-screen and dies. There is also a scene where cows are burned.
Chimpanzee is a documentary so all animal action is real. A young chimpanzee's mother disappears and is presumed killed by a leopard. It appears as though the young chimp will die with no one to care for him but he is eventually adopted by another chimp. Chimps fight each other and kill other monkeys for food but the violence takes place off-screen.
The main character finds his pet hamster dead in the trash after his father kills it
Cold Creek Manor
A little girl's horse is killed with a sheep-killing farm implement and is seen floating in a swimming pool full of bloody water. Also, a deer is hit by a car and a snake is smashed with a rock.
A goat's throat is slit in order for two people to have food to eat. At the end of the movie, a dead baby sheep's coat is placed on an orphan baby sheep so the mother sheep will nurse it, thinking it is her baby.