In cognitive radio (CR) systems reliable spectrum sensing techniques are required in order to avoid interference to the primary users of the spectrum. Whereas most of the existing literature on spectrum sensing considers impairment by additive white Gaussian noise (AWGN) only, in practice, CRs also have to cope with various types of non-Gaussian noise such as man-made impulsive noise, co-channel interference, and ultrawideband interference. In this paper, we propose robust L_p-norm detectors which do not require any a priori knowledge about the primary user signal and perform well for a wide range of nonGaussian noises. Furthermore, we analyze the probabilities of false alarm and missed detection of the proposed detectors in the low signal-to-noise ratio regime. For optimization of L_p-norm detection we propose a direct approach based on minimization of the probability of false alarm for a given probability of missed detection and a simpler approach based on maximization of the deflection coefficient of the detector. Analytical and simulation results show that the proposed L_p-norm detectors achieve significant performance gains over conventional energy detection in non-Gaussian noise.