Aplacental viviparity is a form of egg development in which the eggs of an organism hatch while still inside the uterus but the developing young aren't nourished by a placenta. This form of development is found in many species of shark, stingray, marsupial mammals, and a few species of snake. Aplacental viviparity use to be referred to as ovoviviparity. The term was likely changed to specify that no placenta is present after the embryo emerges from its ovum.
There exist three varieties of aplacental viviparity. The most common form provides nourishment for the developing organism via a yolk sac from its egg and nothing else. The yolk sac is the only source of food for the developing organisms until their live birth (the gestation period varies from species to species), at which point they're usually on their own. Angel sharks, cow sharks, dogfish, frill sharks, tiger sharks, and a number of other species go through this variety of aplacental viviparity during embryonic development.
Another form of aplacental viviparity involves uterine villi, which emerge from a mucous membrane along the walls of the uterus and provide nourishment to the developing organisms in the form of a secretion called histotroph. Stingrays are currently the best example of this form of aplacental viviparity. Fertilised stingray eggs remain in the mother's uterus, ingesting their yolk sacs. Once the embryos have fully consumed their yolk sacs, spatulate villi known as trophomata emerge from the uterine walls and act as a sort of umbilical chord for the developing young. The trophomata secrete histotroph (also called "uterine milk"), a lipid- and protein-rich fluid, and oxygen for the fetuses to ingest and breathe, respectively. Trophomata also carry the fetuses' waste out of the uterus.
The last (and perhaps most interesting) form of aplacental viviparity involves oophagy (eating of eggs) and, in the case of one species, intrauterine cannibalism. This method of egg/fetus development involves the unborn organisms hatching from their eggs sometime within the first three months of gestation to feed upon other ovluated eggs which either haven't been fertilised or have yet to hatch. Lamnoid sharks' (sharks of the order Lamniformes, such as the Great White) ovaries produce thousands of garden pea-sized ova, each enclosed within a case. The embryos within the ova rapidly consume their yolk and begin dentition. After primitive teeth have formed, the embryos break out of their egg cases and feed upon other ova within the uterus.
Sand tiger sharks are noteable amongst all other species which develop this way because the fetuses don't limit themselves to feeding on yolk and unhatched ova. By the time a sand tiger is 30mm long, it has budding teeth. By the time a sand tiger is 60mm long, multiple rows of teeth will have grown in. Sand tiger fetuses are the only fetuses known to eat other, smaller fetuses while in the uterus. This intrauterine cannibalism or embryophagy ensures that only one sand tiger fetus will remain in a uterus by the time the creature is ready to be borne and that the creature will be relatively large at birth (possibly over a metre long). Sibling rivalry at its tastiest.
Sources
http://www.nd.edu/~whamlett/wch_research.htm
http://www.flmnh.ufl.edu/fish/Organizations/SSG/9Newsletter/shark9news1.htm
http://www.enchantedlearning.com/subjects/sharks/anatomy/Repro.shtm
and many other webpages with the same information in little chewed up bits and pieces