Well, off of my head I can think of cats, dogs, snakes, toads,owls and mice which have been used as familiars. Also, observing birds was commonly used as a form of divination, and Power/Spirit/Totem animals seem to be a quite popular form of teaching.
The only inividual animal I can think of is probably the puma or "ghost cat" which amassed a great deal of respect and superstition due to its elusive nature. However, the only thing really "magical" about it is the properties and qualities given to it through shamanism, nothing nearly so drastic as the example stated by krollusk.