The application of an inexact Newton method to two- and three-dimensional flows is described. Robustness and efficiency of the method is largely determined by the preconditioner. A linear multigrid preconditioner that employs classical pressure-correction methods as smoothers is described. The flexibility of the approach is demonstrated through application to both steady and unsteady problems; use of a low-order discretization in the preconditioner; use of mesh sequencing to address the problem of obtaining a good starting approximation for the inexact Newton method; and implementation and performance on parallel computers.