And, depending on location, consider indigenous animals that give zest to places around the world. In some cities, monkeys swing through trees, or parrots fly overhead, or oxen are a common sight. As natural and unassuming as the wind, animals give life to the world.
No matter where your character goes—except maybe in space—there will be animals. In the fields, there are insects chirping, birds flying overhead, and snakes slithering underfoot. In the city, there are rodents that scamper along building walls (remember: squirrels are rodents too!), and neighbors who keep strange exotic pets.
Creative fiction does not need to be in a “real” world, but it does need to be realistic. If realistic, your fiction writing will be believable. A written world is not a believable world if it disregards animals.