Low-resolution analog-to-digital converters (ADCs) have emerged as an efficient solution for massive multiple-input multiple-output (MIMO) systems to reap high data rates with reasonable power consumption and hardware complexity. In this paper, we study precoding designs for digital, fully connected (FC) hybrid, and partially connected (PC) hybrid beamforming architectures in massive MIMO systems with low-resolution ADCs at the receiver. We aim to maximize the spectral efficiency (SE) subject to a transmit power budget and hardware constraints on the analog components. The resulting problems are nonconvex and the quantization distortion introduces additional challenges. To address them, we first derive a tight lower bound for the SE, based on which we optimize the precoders for the three beamforming architectures under the majorization-minorization framework. Numerical results validate the superiority of the proposed precoding designs over their state-of-the-art counterparts in systems with low-resolution ADCs, particularly those with 1-bit resolution. The results show that the PC hybrid precoding design can achieve an SE close to those of the digital and FC hybrid precoding designs in 1-bit systems, highlighting the potential of the PC hybrid beamforming architectures.