Heuristic searches such as A* search are a popular means of finding least-cost plans due to their generality, strong theoretical guarantees on completeness and optimality, simplicity in implementation, and consistent behavior. In planning for robotic manipulation, however, these techniques are commonly thought of as impractical due to the high-dimensionality of the planning problem. As part of this thesis work, we have developed a heuristic search-based approach to motion planning for manipulation that does deal effectively with the high-dimensionality of the problem. In this thesis, I will present the approach together with its theoretical properties and show how to apply it to single-arm and dual-arm motion planning with upright constraints on a PR2 robot operating in non-trivial cluttered spaces. Then I will explain how we extended our approach to manipulation planning for n-arms with regrasping. In this work, the planner itself makes all of the discrete decisions, including which arm to use for the pickup and putdown, whether handoffs are necessary and how the object should be grasped at each step along the way. An extensive experimental analysis in both simulation and on a physical PR2 shows that, in terms of runtime, our approach is on par with some of the most common sampling-based approaches. This includes benchmarking our planning framework on two domains that we constructed that are common to manufacturing: pick-and-place of fast moving objects and the autonomous assembly of small objects. Between these applications, the planner exhibited fast planning times and the ability to robustly plan paths into and out of tight working environments that are common to assembly. The closing work of this thesis includes an exhaustive study of the natural tradeoff that occurs between planning efficiency versus solution quality for different values of the heuristic inflation factor. A comparison of the solution quality of our planner to paths computed by an asymptotically optimal approach given a great deal of time for path optimization is included as well. Finally, a set of experimental results are included that show that due to our approach's deterministic cost-minimization, similar input tends to lead to similarity in the output. This kind of local consistency is important to the predictability of the robot's motions and contributes to human-robot safety.