The stem cells in a baby's umbilical cord blood can be preserved for potential life-saving treatments for the baby or other family members.
Currently, stem cells are being used in transplant medicine to regenerate a patient's blood and immune system after they have been treated with chemotherapy and/or radiation to destroy cancer cells. In the future, stem cells may also be used to improve the treatment of some of the most common diseases such as heart disease, stroke, and Alzheimer's.
Hopefully the cord blood is never needed, but banking it is essentially a form of health insurance.
The only con is the price of banking it. But there are coupons online, for ex:
http://www.cord-blood-banking-coupon.com has one for $250 off.