There are a few private companies in the US, UK and Australia (totally separate from the Cord Blood Banks) who are offering to collect cord blood from babies and store it for 20 years or more, for large fees (generally thousands of dollars). The aim is to keep the cord blood for possible future use by that child in case stem cell research can be further developed to treat other diseases such as heart disease, stroke, Parkinson's, Alzheimer's, Multiple Sclerosis, diabetes, cancer and blood disorders.
The disadvantage for the community with this type of service is that cord blood that could be used to save the lives of ill children today, could be withheld from use 'in case' it can be used in the future by the child who donated it. This type of use for the stem cells in cord blood are possible but at present not a reality. Therefore the blood is not guaranteed of being useful, especially if the treatments are never perfected, or the child does not need it in the first 20 years of their life (which is unlikely, as the diseases aimed at being treated are usually ones relating to old age and are not that common).