The Giant Mechanical Man
An off-screen monkey at a zoo is poked with a stick but there is no mention of it being harmed (we never actually see the monkey). Other zoo animals are seen, none are harmed.
The Glacier Fox
Documentary. A number of foxes die, including a young blind fox that is swept out to sea, a mother fox who bleeds to death after tearing off her foot when it is caught in a trap and a grown fox that is killed by a farmer.
A horse is decapitated and its bloody head used as a gruesome surprise.
The Good Lie
A dead gazelle is seen being eaten by cheetahs (we do not see it being killed).
The Good Neighbor
A dog is threatened with a violent death near the beginning of the movie, but nothing else happens with the dog.
The Good Son
A dog is shot and killed with a crossbow. A cat is almost shot as well, but escapes.
The Grand Budapest Hotel
In a darkly comic scene, a cat is thrown out of a window and is seen splattered on the ground, very dead.
The Green Mile
A mouse is stomped on but is magically brought back to life.
The Green Room
It is implied that a dog will die, but it does not die during the movie.
The Hangover Part II
A monkey that one of the protagonists grew attached to is shot and left in front of a veterinary hospital, and it assumingly survives. The shot doesn't seem to be lethal but needs to be taken care of by a professional. The monkey is also repeatedly depicted smoking cigarettes. Verbal references to bestiality.
The Hangover Part III
A giraffe is decapitated when the open trailer it is in goes under an overpass. Roosters are shot, smothered and thrown out a window. There is mention of dogs being killed off-screen.
Pumpkin the cat, Kevin Garnett the dog and an unnamed drug-sniffing dog each appear in a few scenes; none come to any harm.
The Hebrew Hammer
Aside from having to wear a diaper, nothing bad happens to Mazel Tov the cat.
A pet goldfish dies after being fed an antidepressant.
A dog is taken over by an alien parasite, killing the dog.
The Hills Have Eyes (1977)
Beauty, a German shepherd, is killed and eaten. Another German shepherd, Beast, lives and even returns for the sequel.
A Dalmatian escapes the fire and is listed among the survivors at the end.
The Hobbit: An Unexpected Journey
A pet hedgehog dies from a magical illness but is brought back to life. Trolls threaten to eat several ponies but they all escape. We catch some very brief glimpses of dead forest creatures.
The Hobbit: The Desolation of Smaug
A cat, several dogs and a few mice all appear very briefly; none are harmed. We don't see anything bad happen to any of the horses/ponies and farm animals that also appear. A number of monstrous CGI spiders die, including one whose legs are pulled off.
Charlie the dog does not die and is not hurt, though he doesn't show up in the second half of the film. A stray dog appears in one scene later in the movie, barking at a sewer grate. It disappears but there is nothing to indicate that anything bad happened to it (it could've just run away).
To appease a group of Native Americans that approach a stagecoach, the drivers give them Dorothy, a horse belonging to the main character. After the horse has been taken away, the main character is told that it will probably be eaten (though we don't actually see that happen).
The Horse Whisperer
One horse dies and another is severely injured after a fall and automobile accident.
The Hunger Games
A couple of dogs and a cat appear briefly but the only animals that die are small wild animals that are killed for food (like a bird and a lizard).
The Hunger Games: Catching Fire
Buttercup, the Everdeens' cat, is seen in several scenes and does not die. A few wild animals die, including a rabbit (already dead when we see it), a jabberjay bird (shot with an arrow), and a number of murderous CGI baboons.
Early in the film, a deer is shot and killed. The main character's dog Fanny is killed and delivered wrapped up to her master (Lucas). We don't see what is wrapped up when Lucas first looks but we can guess. However, his son fights to see what it is and then we see it is Fanny. When Lucas is burying his dog, we see several shots of her lying dead on the ground.