The sense, role and some types of crises in social and economic systems is shown in this paper. The comparative analysis of concept and a role of crisis in economic systems from the point of view of the standard economic theory (classical and Keynesian approaches, dynamic models, etc.) and concept of crises in social and economic systems from the point of view of the theory of self-organization are carried out. The difference of concepts of sustainability of system in the specified theories is also shown. Showing that in the existing economic theory crisis is considered as the undesirable phenomenon and, therefore, the primary method of work in this direction are attempts to prevent or suppress crisis. In the theory of self-organization crisis is considered necessary and an unavoidable stage of development of open system. Therefore some of the development trends of the social and economic policy should be: taking the necessity of crisis into account; preparation of the system to the crisis; moving social and economic processes into necessity direction during manifested crisis. The social and economic crises which became frequent recently convincingly testify to need to change of methodological approaches for the analysis of behavior of social and economic systems. New approaches have to consider not only the current stage of development of the system and consider it in dynamics, but also consider structure of the system, and also structure of the processes proceeding in it. The main results of presented research can be useful in further developments of researches in the field of the self-organizing systems, and also to development of some directions of social and economic policy of the state.