The investigators learned that it was possible to generate an immune response in a subset of patients with malignant glioma. In addition, these cells were able to reach the brain and kill brain tumor cells. The survival of patients in this study was prolonged when compared to historical controls. Based on clinical data in subjects with brain tumors, the investigators believe that peripheral injection of dendritic cells will generate a more potent immune response for patients with brain stem gliomas and/or glioblastomas. The investigators hope to determine whether this therapy will translate into a longer survival and better quality of life in these patients in whom survival is measured in months. Through this study the investigators hope to learn more about the role of the body's immune response against cancer and about the use of dendritic cells for immunotherapy. This information may prove useful in the therapy of patients with glioblastoma and/or brainstem gliomas.