This is a question we discuss in class in a couple of different contexts. Courts have traditionally held that animals are "chattels" and that there is no cause of action for emotional distress, loss of companionship and the like when they are injured by others. Usually, if a cause of action is recognized, the injuries are valued based on the "market value" of the animal.
I always ask my students how many of them own pets and ask them to talk about whether they would be affected if their pets were hurt by others (whether intentionally or negligentlly). Invariably a majority of them raise their hands to say they own or have owned pets, that they definitely feel affection for their pets and that injuries to pets do cause their owners sadness, grief and emotional distress.
Now comes news that Vermont's Supreme Court is being asked to decide the issue. In this case, a couple let their dog wander into the defendant's yard and the defendant fatally shot it. The plaintiffs are asking the court to hold that a dog's owners can sue for emotional distress and loss of companionship. For more on the story go here.