The purpose of this paper is to provide new estimates for certain multilevel algorithms. In particular, we are concerned with the simple additive multilevel algorithm given in  and the standard V-cycle algorithm with one smoothing step per grid. We shall prove that these algorithms have a uniform reduction per iteration independent of the mesh sizes and number of levels even on non-convex domains which do not provide full elliptic regularity. For example, the theory applies to the standard multigrid V-cycle on the L-shaped domain or a domain with a crack and yields a uniform convergence rate. We also prove uniform convergence rates for the multigrid V-cycle for problems with nonuniformly refined meshes. Finally, we give a new multigrid approach for problems on domains with curved boundaries and prove a uniform rate of convergence for the corresponding multigrid V-cycle algorithms.