This research study has been designed for people who have been diagnosed with a blood tumor, which has not responded to treatment or has recurred, a bone marrow failure state such as aplastic anemia, or one of certain inherited metabolic disorders; and whose doctor feels the best treatment is an allogeneic stem cell transplant (alloSCT) but a related or unrelated adult donor is not available. Instead, a single unit of umbilical cord blood (UCB) will be used as the source of the subject's immune system. This study is designed to determine whether a single unit of UCB can be substituted for adult bone marrow cells in the standard stem cell transplant regimens used at this hospital for subjects who do not have stem cell donors.