Regulation of stem cell self-renewal versus differentiation is critical for embryonic development and adult tissue homeostasis. Drosophila larval neuroblasts divide asymmetrically to self-renew, and are a model system for studying stem cell self-renewal. Here we identify three mutations showing increased brain neuroblast numbers that map to the aurora-A gene, which encodes a conserved kinase implicated in human cancer. Clonal analysis and time-lapse imaging in aurora-A mutants show single neuroblasts generate multiple neuroblasts (ectopic self-renewal). This phenotype is due to two independent neuroblast defects: abnormal atypical protein kinase C (aPKC)/Numb cortical polarity and failure to align the mitotic spindle with the cortical polarity axis. numb mutant clones have ectopic neuroblasts, and Numb overexpression partially suppresses aurora-A neuroblast overgrowth (but not spindle misalignment). Conversely, mutations that disrupt spindle alignment but not cortical polarity have increased neuroblasts. We conclude that Aurora-A and Numb are novel inhibitors of neuroblast self-renewal and that spindle orientation regulates neuroblast self-renewal.