We made sure to bank the cord blood for our daughter, and later, when that became available, to bank both the cord blood and cord tissue for our son (at double the storage price, natch). The reason is that the blood and the tissue host different types of stem cells, which can differentiate into different tissues later on.
The chances of the baby using the stem cells for themselves within the initial 18-year storage period are infinitesimally low, and we were aware of that. However, working in research, I was aware of studies where stem cells were being used to repair the heart muscle following a heart attack. Extrapolating from that, with full confidence in research and development, we banked all we could bank. Since then, stem cells have been used to grow certain replacement organs for animals, and for humans too. Using the patient's own cells eliminates the need for immune-suppressant drugs. Much more is surely to come, and I didn't want my kids to miss out on the access to life-saving technology (e.g., replacement kidneys, livers, hearts, also cartilage... most people will need some of those in their lifetime) over those initial $3-6000.
There are two caveats to this. First, your kids are not likely to need their cells for many decades. During that time, storage fees need to be paid. The price is only guaranteed for the first 18 years, and after that, the company may charge what they want. The samples may not hold up over time, and you would never know. The technology might change in a way that makes the preparation process used today obsolete. The company might go out of business. Aliens might invade. Etc. Second, and more to the point, we are already at the point where needed stem cells can be harvested from adult tissue, at least for some purposes. This was not the case when we first banked. It is very likely that many decades from now, there would be no need for the banked cells and tissue, and banking will turn out to have been a big waste of money. Technology is amazing. I might still be willing to put up a few thousands as insurance in case banked tissue is actually needed for something. Eighteen years from now, when these contracts come up for renewal, we'll know more and can make decisions accordingly.