Why do animals play such an enduring part in our culture and storytelling? Is it because they have predefined characteristics that help them fit more easily into stereotypical roles? Who hasn't heard of The Three Little Pigs, The Big Bad Wolf, or The Three Bears?
Typical story predators: wolves, foxes, bears, human beings, lions and other big cats, snakes, spiders, alligators, eagles and other raptors, sharks, piranhas, biting insects such as mosquitoes and flies, stinging creatures such as bees, wasps, scorpions, etc.
Typical prey: pigs, sheep, chickens and other domestic fowl, human beings, mice, rabbits, deer, birds of every type, horses, cattle, fish, butterflies and other harmless insects, goats, etc.
Notice that people appear on both lists. Red Riding Hood was potential prey; the hunter in her story needs no introduction to be on the first list.