As an essential approach to understanding human interactions, emotion classification is a vital component of behavioral studies as well as being important in the design of context-aware systems. Recent studies have shown that speech contains rich information about emotion, and numerous speech-based emotion classification methods have been proposed. However, the classification performance is still short of what is desired for the algorithms to be used in real systems. We present an emotion classification system using several one-against-all support vector machines with a thresholding fusion mechanism to combine the individual outputs, which provides the functionality to effectively increase the emotion classification accuracy at the expense of rejecting some samples as unclassified. Results show that the proposed system outperforms three state-of-the-art methods and that the thresholding fusion mechanism can effectively improve the emotion classification, which is important for applications that require very high accuracy but do not require that all samples be classified. We evaluate the system performance for several challenging scenarios including speaker-independent tests, tests on noisy speech signals, and tests using non-professional acted recordings, in order to demonstrate the performance of the system and the effectiveness of the thresholding fusion mechanism in real scenarios.