Techniques are described for managing distributed execution of programs. In at least some situations, the techniques include decomposing or otherwise separating the execution of a program into multiple distinct execution jobs that may each be executed on a distinct computing node, such as in a parallel manner with each execution job using a distinct subset of input data for the program. In addition, the techniques may include temporarily terminating and later resuming execution of at least some execution jobs, such as by persistently storing an intermediate state of the partial execution of an execution job, and later retrieving and using the stored intermediate state to resume execution of the execution job from the intermediate state. Furthermore, the techniques may be used in conjunction with a distributed program execution service that executes multiple programs on behalf of multiple customers or other users of the service.