To investigate critical frequency bands and channels, this paper introduces deep belief networks (DBNs) to constructing EEG-based emotion recognition models for three emotions: positive, neutral and negative. We develop an EEG dataset acquired from 15 subjects. Each subject performs the experiments twice at the interval of a few days. DBNs are trained with differential entropy features extracted from multichannel EEG data. We examine the weights of the trained DBNs and investigate the critical frequency bands and channels. Four different profiles of 4, 6, 9 and 12 channels are selected. The recognition accuracies of these four profiles are relatively stable with the best accuracy of 86.65%, which is even better than that of the original 62 channels. The critical frequency bands and channels determined by using the weights of trained DBNs are consistent with the existing observations. In addition, our experiment results show that neural signatures associated with different emotions do exist and they share commonality across sessions and individuals. We compare the performance of deep models with shallow models. The average accuracies of DBN, SVM, LR and KNN are 86.08%, 83.99%, 82.70% and 72.60%, respectively.