Motivated by the recent discovery of superconductivity in infinite-layer nickelate thin films, we report on a synthesis and magnetization study on bulk samples of the parent compounds RNiO₂ (R = La, Pr, Nd). The frequency-dependent peaks of the alternating current magnetic susceptibility, along with remarkable memory effects, characterize spin-glass states. Furthermore, various phenomenological parameters via different spin glass models show strong similarity within these three compounds as well as with other rare-earth metal nickelates. The universal spin-glass behaviour distinguishes the nickelates from the parent compound CaCuO₂ of cuprate superconductors, which has the same crystal structure and d⁹ electronic configuration but undergoes a long-range antiferromagnetic order. Our investigations may indicate a distinctly different nature of magnetism and superconductivity in the bulk nickelates than in the cuprates.