Caenorhabditis elegans exhibits spontaneous motility in isotropic environments, characterized by periods of forward movements punctuated at random by turning movements. Here, we study the statistics of turning movements-deep Omega-shaped bends-exhibited by swimming worms. We show that the durations of intervals between successive Omega-turns are uncorrelated with one another and are effectively selected from a probability distribution resembling the sum of two exponentials. The worm initially exhibits frequent Omega-turns on being placed in liquid, and the mean rate of Omega-turns lessens over time. The statistics of Omega-turns is consistent with a phenomenological model involving two behavioral states governed by Poisson kinetics: a "slow" state generates Omega-turns with a low probability per unit time; a "fast" state generates Omega-turns with a high probability per unit time; and the worm randomly transitions between these slow and fast states. Our findings suggest that the statistics of spontaneous Omega-turns exhibited by swimming worms may be described using a small number of parameters, consistent with a two-state phenomenological model for the mechanisms that spontaneously generate Omega-turns.