Direct-conversion radio (DCR) receivers can offer highly integrated low-cost hardware solutions for spectrum sensing in cognitive radio (CR) systems. However, the DCR receivers are susceptible to radio frequency (RF) impairments, such as in-phase and quadrature-phase imbalance, low-noise amplifier nonlinearities, and phase noise, which limit the spectrum sensing capabilities. In this paper, we investigate the joint effects of RF impairments on energy detection-based spectrum sensing for CR systems in multi-channel environments. In particular, we provide the novel closed-form expressions for the evaluation of the detection and false alarm probabilities, assuming Rayleigh fading. Furthermore, we extend the analysis to the case of CR networks with cooperative sensing, where the secondary users suffer from different levels of RF imperfections, considering both scenarios of error free and imperfect reporting channel. Numerical and simulation results demonstrate the accuracy of the analysis as well as the detrimental effects of RF imperfections on the spectrum sensing performance, which bring significant losses in the spectrum utilization.