Pica is a medical condition veterinarians sometimes encounter in practice. Pica comes from the latin word for magpie, a bird with a reputation for eating almost anything. Pica is considered a symptom of disease (like vomiting or fever, for example), not a disease per se. Pica can be exhibited by dogs and cats suffering from a plethora of medical conditions, from gastrointestinal parasites, to anemia, to liver disease, to cancer. While most humans who exhibit pica have serious mental illness (OCD, schizophrenia, etc), dog and cats almost invariably have a physical condition, often a lack of a dietary requirement or nutrient of some kind, or any disease that results in a loss of nutrients from the body. Anemia (absolute decrease in red blood cells and hemoglobin) is a very common cause of pica. Anemia, like pica, is not a disease but a reflection of disease. Many, many diseases result in anemia: gastrointestinal parasites (especially hookworm infestations), iron-deficiency, auto-immune diseases, blood parasites, hemorrhage of any kind (especially GI ulceration), and cancer. All of these conditions, and others, can result in pica.
Patients with liver shunts (essentially, blood from the intestine doesn't go to liver but bypasses it) sometimes exhibit pica. In a nutshell, the animal is trying to make up for what cannot be produced by the liver, since the liver is not receiving nutrients from the gut.
One very recent case I saw involved a cat with true red blood cell aplasia, a rare auto-immune disorder where the immune system destroys the red blood cell precursors in the bone marrow. This cat swallowed a few shoe laces and elastic bands - you really had to see it to believe it. The objects in the poor cat's stomach were the least of his problems.
Now, can magpies suffer from pica?
X-ray from a mentally ill man with pica. The large white area on the radiograph is a collection of hundreds of coins, needles and other objects not typically eaten by healthy men. The whole story here.