When in doubt, Animal it out.
If you've read any of my books, you've probably noticed the animals in them—as pets, as background, or as a plot device.
Animals in fiction, whether for novels, television, or film are an extremely valuable tool. For one, their presence is pleasing to the audience—and who doesn't want to please their audience? They elicit emotion in the reader, bolster engagement. I mean, look at the picture on the right. Does it elicit emotion out of you? Or are you just a psychopath?
Animals can aid your characterizations while following that ever important show vs tell. For example, the type of pet you assign your character can reveal a lot about them. Just like it does in real life.
You might assign a golden retriever to a character you are trying to portray as extroverted and fun, or give a tarantula to a character who feels detached and misunderstood. Animals can also be used to show transformation. Like say, if your hardened, gruff character needs to evolve into a softer, more open character, they could find themselves suddenly allowing a stray dog into their house.
Animals are great for breaking up tension in a scene or for balancing the overall tone of your book or movie. Is your book too intense? Add a dog to give readers an emotional break. Animals are also useful to move along the plot, to reveal plot, or for misdirection. Master filmmaker Steven Spielberg uses the misdirection technique in his movie E.T.. Elliot goes into his backyard, searching for his dog. We hear a noise, and Elliot follows it, thinking he'll find his beloved pet. Instead, he finds E.T.. In Poltergeist, which Spielberg wrote, the dog is used both to move plot and reveal it. The dog, through barking and whining, alerts the characters (and the audience) multiple times that something isn't quite right in the house, thus building tension.
Think an animal wouldn't fit into your story? Think again. Ever watch Alien? They put a cat on a space ship in the middle of space. So if they can do that, it's not impossible for you fit an animal into your story.
Just be careful, though, if you decide to kill a pet or other animal in your project. I've known readers who were so put off by the death of an animal in a story, they put the book down and never picked it up again. So please, use animals to breath life into your works, but use them wisely.