We consider the numerical solution of the stationary incompressible Navier-Stokes equations for a wide range of Reynolds numbers by a nonconforming finite element discretization of upwind type in primitive variables. For solving the discrete systems of equations within an outer nonlinear iteration, we propose an efficient and robust multigrid algorithm which admits a slightly modified parallel version with nearly the same good properties. The multigrid method is based on a blockwise Gauss-Seidel smoother where each block is determined by the unknowns of a finite element. For the parallelization, we decompose our domain into macroelements which are the finite elements of the coarsest grid level.