I have a friend who sometimes sees the spirits of dead pets. Her brother sometimes sees the spirits of animals. For instance, when her brother was two or three, their family was at a cabin. A man had shot himself recently and he had had a swinget in his yard. My friend's brother had been swinging on it (his mom was watching him and my friend hadn't been born yet) and even though he could barely talk, he had suddenly said, "Mommy, there's a man. There's a man, and (pause) he shot himself..." Creepy, eh?
Once my friend had been laying on the couch and suddenly a dog had ran down the hall. She felt like it was protecting her. When it left, the feeling of protection went away and later, her mom told her the dog's name. Sometimes, she sees dogs, and when she describes them to her mom, her mom tells her their names, because they were dogs that she had owned. There were others that she told me, but I have forgotten them. However, even though she usually sees dead animals when she sees spirits, once she heard the cookie jar lid lifting up and she thought it was her brother stealing cookies. When she went in there, she saw her dead grandfather, who had loved cookies. She left a letter for him and it disappeared. I have no proof of any of these, but my friend swore that they are true. She is not the sort of person who would lie about things like this.