The Day of the Dolphin
Two dolphins, Alpha and Beta, are trained for good purposes but then stolen and used for an attempted assassination plot. Both dolphins survive, though that doesn't necessarily mean the movie has a happy ending.
The Deadly Bees
A dog is killed by bees; the death happens off screen but we see the dead dog afterward.
The Dog Problem
A dog is bitten by another dog and has to go to the vet. He recovers.
The Drawn Together Movie: The Movie!
Several cute animal babies are brutally and gorily stomped to death in an extended, graphic scene. The Road Runner is run over and dies, and Wile E. Coyote shoots himself, not seeing any further meaning in his life. A dinosaur is shot in the back and it falls down to the floor, but we don't know if it's dead or just hurt.
Rocco the pit bull puppy is rescued from a trash can at the beginning of the film. Though he is threatened during the film, he ends up living happily ever after with his rescuer.
A rat is killed and eaten raw by a man. A horse falls over from exhaustion and is left behind (its death is not seen). Dogs are seen in several scenes but none die.
The Extraordinary Adventures of Adèle Blanc-Sec
Though he is carried away by a pterodactyl, Nelson the Scottie dog does not die. However, the pterodactyl (which starts out as an antagonist but soon becomes friendly with Adèle) is later shot and killed. A sheep is also shot but we hear someone call for a vet and we don't see it die.
A German shepherd is shot and killed off screen; the body is seen.
Oscar the rat is assimilated by an alien organism and then has his neck broken out of mercy.
The family dog seems like it's dying in a gun battle but ends up living.
A dog's back is broken and it dies painfully and slowly on camera before it is thrown overboard.
The Fly II
A dog is mutated, becomes deformed and violent, is studied and eventually killed. Another dog is later spared by the Fly.
It is implied that two dogs die offscreen.
The Fox and the Hound
Animated. Tod the fox and Copper the dog do not die. Tod's mother is shot and killed offscreen by hunters in the first few minutes of the film. Chief the dog falls and is injured but recovers. Tod and Copper are both injured in a fight with a bear; they survive but it appears as though the bear doesn't.
Rustler the ghost dog is shot at but not hurt (he's already dead).
Paw-Paw, a cat waiting to be adopted by the main characters in the film, is euthanized because his new owners forget to pick him up.
The Gangs Of New York
There are several dogs shown in the movie, but none of them are killed or die. A few rats are killed by one of the dogs in a betting game. Towards the end of the movie, a exotic museum is burned down and you can hear monkey's and other animals screaming
A dog dies and its corpse is seen (and danced with). Later the corpse is carried around and after it is buried, it appears in a child's bed. At the end of the film it turns out that the dog is alive after all. Also, some moths are shaken in a jar.