In this paper, we introduce a new Differentiated Successive Interference Cancellation (DiffSIC) ordering technique for up-link multi-user Multiple-Input Multiple-Output (MIMO) systems. Unlike classical SIC, DiffSIC is capable of differentiating users according to their priority or class of service by selecting a detection order that best fits the users' service profiles. In addition, DiffSIC is able to achieve the optimal SIC detection order that results in the best overall system performance. In order to develop DiffSIC, we introduce analytical methods towards finding instantaneous symbol error rates (SER) for the Zero Forcing SIC (ZF-SIC) and Minimum Mean Square Error SIC (MMSESIC) detectors. We present a number of numerical results which clearly demonstrate the ability of DiffSIC to accomplish service differentiation and overall performance improvement in general.