This paper advocates the use of self-stabilization as a provable property to achieve the goals of the self-* paradigms for systems, including availability, reliability, serviceability, disaster recovery and autonomic computing. Several recent results starting from hardware concerns, through the operating system, and ending in the applications are integrated: the self-stabilizing microprocessor [10, 11], with a self-stabilizing operating system [27, 28, 29, 30], the self-stabilizing file system [18], the self-stabilizing middleware [24, 25, 26, 19], the self-stabilization preserving compiler [12], the self-stabilizing autonomic recoverer for applications [2], and at last the combination of the local recovery and the self-stabilization properties to obtain self-organizing systems [21, 22].