In the real world, the execution of the actions planned for an agent is never guaranteed to succeed, as they can fail in a number of unexpected ways that are not explicitly captured in the planning model. Based on these observations, we introduce the task of finding plans for classical planning that are resilient to action execution failures. We refer to this problem as Resilient Planning and to its solutions as K-resilient plans; such plans guarantee that an agent will always be able to reach its goals (possibly by replanning alternative sequences of actions) as long as no more than K failures occur along the way. We also present RESPLAN, a new algorithm for Resilient Planning, and we compare its performance to methods based on compiling Resilient Planning to Fully-Observable-Non-Deterministic (FOND) planning.