In this paper, we investigate stable patterns of electroencephalogram (EEG) over time for emotion recognition using a machine learning approach. Up to now, various findings of activated patterns associated with different emotions have been reported. However, their stability over time has not been fully investigated yet. In this paper, we focus on identifying EEG stability in emotion recognition. We systematically evaluate the performance of various popular feature extraction, feature selection, feature smoothing and pattern classification methods with the DEAP dataset and a newly developed dataset called SEED for this study. Discriminative Graph regularized Extreme Learning Machine with differential entropy features achieves the best average accuracies of 69.67 and 91.07 percent on the DEAP and SEED datasets, respectively. The experimental results indicate that stable patterns exhibit consistency across sessions; the lateral temporal areas activate more for positive emotions than negative emotions in beta and gamma bands; the neural patterns of neutral emotions have higher alpha responses at parietal and occipital sites; and for negative emotions, the neural patterns have significant higher delta responses at parietal and occipital sites and higher gamma responses at prefrontal sites. The performance of our emotion recognition models shows that the neural patterns are relatively stable within and between sessions.