Background: - Cord blood is blood that is taken from the umbilical cord and placenta of healthy newborns after childbirth. The cord blood collected from a baby is called a cord blood unit. Cord blood units are stored frozen in public cord blood banks. About 10,000 cord blood transplants have been performed in children and adults for blood cancers and other diseases in the world. These transplants have helped save lives and improve treatments. However, not all available units of cord blood have been collected, stored, and licensed according to specific government requirements. These unlicensed units can still be used in transplant, but they can only be given as part of specific research studies. This study will evaluate the safety of giving these unlicensed units by recording any problems that may occur during and after giving the cord blood. Objectives: - To test the safety and effectiveness of unlicensed cord blood units in people who need stem cell transplants. Eligibility: - Individuals who are scheduled to have a stem cell transplant. Design: - Participants will be screened with a medical history and physical exam. - Participants will receive the cord blood unit as part of their stem cell transplant procedure. The transplant will be performed according to the current standard of care for the procedure. - After the transplant, participants will be monitored for up to 1 year. Any problems or side effects from the transplant will be treated as necessary. All outcomes will be reported to the National Cord Blood Program and to the Center for International Blood and Marrow Transplant.