According to WebMD, dogs can eat the fruit of a peach but not the pit because it can cause inflammation of the small intestines. The pits of plums, persimmons and peaches also contain cyanide, which is poisonous to both animals and humans.
Along with peach pits, there are a variety of fruits a dog should never eat, including grapes and raisins. Grapes and raisins can cause renal failure, and even just a small amount can make a dog very sick. According to WebMD, some of the fruits a dog can safely eat include apples, oranges, bananas and even watermelon after the seeds and stems have been removed.