The numerical simulation of three-dimensional dam break flows is discussed. A non-hydrostatic numerical model for free-surface flows is considered, which is based on the incompressible Navier-Stokes equations coupled with a volume-of-fluid approach. The numerical results obtained for a variety of benchmark problems show the validity of the numerical approach, in comparison with other numerical models, and allow to investigate numerically the non-hydrostatic three-dimensional effects, in particular for the usual test cases where hydrostatic approximations are known analytically. The numerical experiments on actual topographies, in particular the Malpasset dam break and the (hypothetical) break of the Grande-Dixence dam in Switzerland, also illustrate the capabilities of the method for large-scale simulations and real-life visualization.