The idea that poinsettias are poisonous most likely dates to the early 20th century, when the death of a two-year-old child was attributed to eating a poinsettia leaf. Since then, public health authorities have struggled to right the record: poinsettias are NOT poisonous and they pose no danger to pets or children.
The poinsettia belongs to the Euphorbia genus. While there are some very toxic Euphorbias, poinsettias are not among them. According to POISINDEX—the service used by every poison control center in the United States—a 50 lb. child would have to eat more than 500 poinsettia leaves to even begin approaching toxic levels.
In 1996, researchers from the Children's Hospital of Pittsburgh conducted the largest scientific survey of poinsettia toxicity that I could find. Here are the results: they examined 22,793 cases of supposed poinsettia poisoning as reported to the American Association of Poison Control Centers. Of these, 99% were accidental, and 93.3% involved children. Ninety-six percent of the children needed no treatment and suffered no symptoms.
The greatest risk posed by the poinsettia is a skin reaction to the plant's milky white sap. This is called contact dermatitis, and it can occur in people who are naturally sensitive to plants in the Euphorbia genus (which includes milkweed). For this reason, it's probably best to avoid the sap whenever possible and to wash your hands thoroughly after exposure. Also, eating poinsettia leaves might result in a stomachache—but this is most likely true of any plant, and some houseplants truly are dangerous. Children should be taught to avoid eating any plants, including poinsettias.
But rest assured: your beloved holiday poinsettia poses no risk to your pets and your children.