Parthenogenesis -- when eggs develop into embryos without being fertilized by sperm -- occurs in some insects and reptiles. There is a persistent report that a virgin birth once took place in humans, but this should be regarded as mythical.
Very rarely, eggs do develop parthenogenetically in humans, but the resulting embryo either dies or turns into an ovarian tumor. It is precisely this aspect of parthenogenetic human embryos that makes them interesting to many biologists, because their inviability frees them from the legal problems and pro-life controversies that surround the cloning of human embryos.
All embryos are special because they contain stem cells: cells that are "pluripotent," or able to become any of the body's varied cell types -- muscle, nerve, skin, heart -- you name it. Stem cells from your own body would, in theory, enable you to develop any new organ or repair any damaged one. Their use, say some researchers, would be a more effective treatment for many diseases than all other forms of therapy combined: They could potentially revolutionize medicine.