Computing systems have become so complex that the IT industry recognizes the necessity of deliberative methods to make these systems self-configuring, self-healing, selfoptimizing and self-protecting. Architectures for system self-management, also called Autonomic Computing (AC), have been proposed where elements are managed by monitoring and analyzing behaviors and using the response to plan and execute new actions that take or keep the system in desirable states. In this paper, we explore the planning needs of AC, its match with existing planning technology and its connections with policies and planning for web services and scientific workflows (grids). We show that planning is an evolutionary next step for AC systems that use procedural policies today. This connection also raises interesting research problems in adapting automated planning techniques to AC applications.