I'm divided on this issue.
The best thing would be if everyone put their cord blood into a public bank. The changes that one child would need cord blood are miniscule, especially as medical technology is just developing in this field.
But the chancs that some child out of 7 million people would need cord blood are much bigger. And if everyone donated, there should be enough for all ill children, including your own, in case of that rare, unfortunate occurance.
With my first child, I tried to donate to the Red Cross, but it's very limited here. They only extra from specific public hospitals at specific times.
I then called some of the blood-banking companies to ask if I could pay for the extraction and transfer, but have it sent to the Red Cross. As soon as the salespeople heard I wouldn't be paying for, like, 20 years of rental, they hung up on me. This left a bad taste in my mouth that - really - they don't care about sick kids, just your long-term business.
That said, now expecting my second child, I do wonder if I would regret it if one of my children unfortunately become that rare child who could use cord blood someday -- and I didn't store it now.