Here is a link to an absolutely amazing video of a baby being born with the amniotic sac still intact: http://www.youtube.com/watch?v=3npxGfBHWbk
Baby Born at Baby Love Birth Center in Cape Coral, FL.
The "bag of waters" stays intact until the baby is born and baby is born "in caul", which is said to confer special sight to a baby. Due to the impatience of modern obstetrics, most babies have their sacs"broken" during labor [routinely,] in the theory [repeat: theory] that birth will occur faster. We prefer to leave moms and babies undisturbed. I would like for people to see what is possible when you leave things as nature intended. Baby was born healthy, 7 pounds 5 ounces.
Being born in the caul -http://en.wikipedia.org/wiki/Childbirth#Being_born_in_the_caul