This is something a woman's obstetrician should discuss with her during pregnancy. Some women choose to donate the cord blood to the national bank where it can be used by anyone who matches it. This type of donation is free, but if your child or family member gets sick down the road, you run the risk of the blood having been used for someone else in the meantime.
Other women choose to bank the cord blood, saving it in their name for the future, in case the child or anyone in the family needs it. This type of donation costs quite a bit of money - I believe about $2,000 for the initial collection and preservation, and then maybe a hundred or so dollars a year for LIFE to keep the blood banked safely. The benefit from this, though, is that the blood is your possession and it won't be used unless you ask for it.
Either way, the doctor NEEDS to know this before delivery. There are special techniques and kits they have for removing all the cord blood and things need to be set up during labor, I believe.
I personally plan to donate my cord blood to the national bank for anonymous usage, if my obstetrician agrees to do the collection. I agree that it should be done more often because it's a waste of perfectly good blood that could save lives, and if you do the free donation, it's better than just letting it be thrown out!
HOWEVER, about using it for regular transfusions - this is not what I'm talking about. Cord blood is full of stem cells, and the transfusion of cord blood has been shown to actually CURE many kinds of cancer and neurological problems in people, especially children. It's now considered to be even better than bone marrow transplant for cancer patients. It's much more valuable than regular blood!!!!!!!!!!!!!!