The purpose of this study is to test the safety and effects of a special type of a cancer vaccine called a 'dendritic cell vaccine' in patients with either newly diagnosed or recurrent glioblastoma. The goal of this dendritic cell vaccine is to activate a patient's own immune system against their tumor. This study utilizes a patient's own immune-stimulating dendritic cells that are isolated in a procedure called leukapheresis. In a laboratory, these dendritic cells are treated in a way that is designed to promote an immune response against cancer stem cells. Then the dendritic cells are injected under the skin in a series of vaccinations, with the goal of activating an immune response against cancer stem cells in the tumor.