In less than three decades, several paradigms of social computing have emerged. Among them, groupware, social software and mobile social software (MoSoSo) are the most widely known. Although all significant, it is challenging to recognize the function and unique features of each single paradigm. This situation represents an obstacle for a coherent development of social computing, a research domain that is highly fragmented and with relevant literature spread across several disciplines. In this paper, a classification of existing social computing paradigms is introduced as an initial effort to combine the lines of discourse concerning social computing.