For my hangout on pets in worldbuilding I was joined by Dale Emery, Glenda Pfeiffer, Jaleh Dragich, Janet Harriett, and Harry Markov.
We started out by talking about how pets are deeply integrated into our culture. The simple fact that we have so many people posting cat and dog photos or videos on the internet says a great deal about their importance, as does the fact that almost anyone can be ready to engage on the question of whether you are "a cat person" or "a dog person." For those who are wondering, I'm a cat person. Jaleh mentioned horses, and while those are too big to be considered house pets, they did bring up a rather interesting idea: that of the coevolution of domesticated species and humans (the linked article mentions dogs but focuses more on horses).
According to what I've read in National Geographic, on the internet and elsewhere, it's looking like early humans didn't go out and deliberately domesticate these animals. Instead, the animals came around human communities because food was more easily obtainable there, and the people started interacting with them, deliberately caring for them (naming them, as Janet mentioned) and taking advantage of their natural traits as hunters.
Dale came in at that point with a wonderful example of the cultural significance of pets from a scene he designed, where a runaway boy who has just obtained a sandwich meets another boy who has a dog; the runaway offers half his sandwich to the boy with the dog, and is rather offended when the boy with the dog splits his half in half and gives half of it to the dog. The idea of course being that the dog has a kind of value to the boy keeping him that the runaway boy simply doesn't grasp.
Returning to the topic of National Geographic, we then discussed the example of the fox-breeding experiments, where scientists have found that foxes can be bred to be instinctively friendly to humans, unlike, say, big cats, who can only be friendly to humans if they are taught to do so since kittenhood, but whose friendliness will not be passed on to the next generation. We speculated that in dogs the affinity for humans might be an alteration of the pack instinct, while in cats it might be a sort of neoteny (thanks Dale for the word) where kittenhood characteristics are retained into adulthood.
There are all kinds of cultural references to dogs, cats, and other animals which are kept as pets. The dog is "man's best friend." The cat "used to be worshipped in ancient Egypt and never got over it." People can be described as dog or cat people. Snakes can be seen as scary or sexual (due to the imagery of the serpent in the garden of Eden, but they are kept as pets and have a lot of metaphorical significance (I'll return to this). Someone recommended Vonda McIntyre's Dreamsnake in which snakes where familiars and assistants. Other unusual pets were mentioned, including crickets in China, and horses, and birds. It's also good to consider whether the humans in the world you are building have working animals like herding dogs, cattle dogs or sight hounds - or hawks. Glenda mentioned that in a bare subsistence lifestyle, pets might be less common unless they have additional utility as working animals.
You can also really help the sense of richness in your world by considering what types of qualities are associated with particular animals - we often use dogs to represent faithfulness and loyalty, cats for grace and nobility, but we also will use dogs as an insult to people we don't like. In Varin, people will say that someone is selfish as a cat - cave-cats are large, selfish and threatening. Calling a person a tunnel-hound refers to the tendency of the eyeless tunnel-hounds to snuffle all over people (it implies that they are fawning); one can also describe a person as "defensive as a tunnel-hound" because they are notoriously tough when cornered before their dens. Note, however, that though the Varini keep tunnel-hounds as working animals, they don't keep them as pets because they're not good-looking enough. Instead they typically keep birds or ferrets.
If you're looking for books with animals in them, you can go to Jack London for dogs (and some of the problems with them!). Dean Koontz writes of superintelligent telepathic dogs, and Andre Norton includes cats. Anne McCaffrey's work features the working watchwhers, and the firelizards, who are great pets but only if they are impressed upon hatching.
We made a list of "pets that suggest special things about the people keeping them": Siamese cats, Falcons, Corgis, Cavalier King Charles Spaniels, Shih Tzu dogs, racing dogs. I would include "evil villain cats" in this list, which are traditionally long-haired but can also be hairless. This kind of thing - i.e. the idea that the keeping of a particular type of pet informs people about your identity or character or socioeconomic status - is something that can be very flavorful in worldbuilding.
Harry Markov told us about dogs in Bulgarian culture, where herding has been very important for hundreds of years. The traditional good dog's name is not "Fido" there but "Sharo" - a Sharo is a bit like a "Lassie." There has been a long tradition of shepherds with dogs in the villages, and livestock is still very popular (sheep, cattle, goats). As a result, there are lots of stray dogs on the streets and not enough adoptions, to the point where you can have problems with dangerous street dogs. Dogs on the street are seen as both positive and negative. People will feed the wild dogs while they have snacks. The dogs learn as a result how to cross streets, and where to go to get the best food. (Janet remarked at this point that she has heard that some dogs know how to navigate the Moscow subway.) The other interesting aspect of the culture surrounding dogs in Bulgaria is that most people don't care if their dog is a mutt, and many more people adopt strays and keep mixed-breed dogs than keep pure-blooded dogs. I was reminded of the city animal populations of cats and crows in Tokyo, and the spoiled deer in the city of Nara. If you're looking for an element of interest for a city you're working with, you might consider whether there is a native animal population alongside your people.
As a few final thoughts we talked about Canada geese and how they have become so populous in some communities that they are being herded off golf courses by dogs, about elephants that are used for transportation, cows in India that may or may not be considered sacred depending on which religion you hold, fish, and rats (rats have their own complexity, being symbols of dirt but also highly intelligent, kept as pets and used in labs).
I enjoyed the discussion. This week's worldbuilding hangout will be on this coming Wednesday, the 14th of March at 11am PDT (watch for the time change, international folks, because if you're not careful you'll miss it! We're an hour earlier from here on into the summer.) We'll be talking about Swearing, so that should be a very colorful conversation. I look forward to seeing you!