Thank you for having a service like this and taking the time to consider our question.
B'H my wife and I are expecting our first baby. We have been hearing a lot about cord blood banking and would like to understand the halachik views on the issue and the different considerations regarding family banking vs. anonymous donation.
Thank you again and we look forward to your response.
Please see response of Rabbi Dr. Mordechai Halperin on this topic (IRP Responsum #3098).
In summary, there is a benefit in umbilical cord blood donation both for the child and for relatives or others who may need bone marrow transplants. There are neither moral nor halachic contraindications, except for on Shabbos, when there is room for further discussion and details if the procedure will be done by a Jewish physician or nurse. (Rav Halperin's discussion about burial of the placenta is not relevant for your question.)
Family donation ensures the availability of the blood cells for the child or family members, but carries a significant financial cost, as any other "insurance policy." Since the likelihood of needing the blood cells is low, one is not required to make this financial investment. If the family decides not to do so, it is appropriate to donate the cord blood to an anonymous bank, since it may save lives of others.