We present a state-space generalized linear model (SS-GLM) for characterizing neural spiking activity in multiple trials. We estimate the model parameters by maximum likelihood using an approximate Expectation-Maximization (EM) algorithm which employs a recursive point process filter, fixed-interval smoothing and state-space covariance algorithms. We assess model goodness-of-fit using the time-rescaling theorem and guide the choice of model order with Akaike's information criterion. We illustrate our approach in two applications. In the analysis of hippocampal neural activity recorded from a monkey performing a location-scene association task, we use the model to quantify the neural changes related to learning. In the analysis of primary auditory cortex responses to different levels of electrical stimulation in the rat midbrain, we use the method to analyze auditory threshold detection. Our findings have important implications for developing theoretically-sound and practical tools to characterize the dynamics of spiking activity.