Recent evidence from functional magnetic resonance imaging suggests that cortical hemodynamic responses coincide in different subjects experiencing a common naturalistic stimulus. Here we utilize neural responses in the electroencephalogram (EEG) evoked by multiple presentations of short film clips to index brain states marked by high levels of correlation within and across subjects. We formulate a novel signal decomposition method which extracts maximally correlated signal components from multiple EEG records. The resulting components capture correlations down to a one-second time resolution, thus revealing that peak correlations of neural activity across viewings can occur in remarkable correspondence with arousing moments of the film. Moreover, a significant reduction in neural correlation occurs upon a second viewing of the film or when the narrative is disrupted by presenting its scenes scrambled in time. We also probe oscillatory brain activity during periods of heightened correlation, and observe during such times a significant increase in the theta band for a frontal component and reductions in the alpha and beta frequency bands for parietal and occipital components. Low-resolution EEG tomography of these components suggests that the correlated neural activity is consistent with sources in the cingulate and orbitofrontal cortices. Put together, these results suggest that the observed synchrony reflects attention- and emotion-modulated cortical processing which may be decoded with high temporal resolution by extracting maximally correlated components of neural activity.