Centrioles are ancient organelles that build centrosomes, the major microtubule-organizing centers of animal cells. Extra centrosomes are a common feature of cancer cells. To investigate the importance of centrosomes in the proliferation of normal and cancer cells, we developed centrinone, a reversible inhibitor of Polo-like kinase 4 (Plk4), a serine-threonine protein kinase that initiates centriole assembly. Centrinone treatment caused centrosome depletion in human and other vertebrate cells. Centrosome loss irreversibly arrested normal cells in a senescence-like G1 state by a p53-dependent mechanism that was independent of DNA damage, stress, Hippo signaling, extended mitotic duration, or segregation errors. In contrast, cancer cell lines with normal or amplified centrosome numbers could proliferate indefinitely after centrosome loss. Upon centrinone washout, each cancer cell line returned to an intrinsic centrosome number "set point." Thus, cells with cancer-associated mutations fundamentally differ from normal cells in their response to centrosome loss.