We present a numerical model for the simulation of free surfaces flows, with multiple, incompressible, immiscible, Newtonian phases. Such multiphysics problems involve both interfaces between fluids and free surfaces between fluids and a surrounding vacuum. We consider flows with strong interface effects, including surface tension forces, and with or without contact angles on the free surfaces. We advocate an Eulerian modeling of the multiphase flows, relying on the volume-of-fluid (VOF) method to describe multiple phases. We enforce surface tension forces on the interfaces between all phases and on the free surfaces, and we impose contact angles with the rigid walls. One advantage of the Eulerian approach is to allow for large deformations and changes of topologies. The numerical framework relies on an operator splitting strategy and a two-grid method. The operator splitting strategy allows to decouple the transport operators from the diffusion problems. The space discretization relies on a structured Cartesian grid, and an unstructured finite element mesh. An adaptive mesh refinement method is advocated in the neighborhood of the interfaces to accurately impose surface forces. The prediction step allows to solve the transport equations with a method of forward characteristics on the Cartesian grid. The correction step consists of solving a generalized Stokes problem, using low order piecewise linear finite elements. The numerical model is validated with several numerical experiments. We focus first on the influence of contact angles in the simulation of hydrophilic and hydrophobic droplets. Finally, we address the simulation of emulsion processes in food engineering, for which surface tension effects induce the creation of droplets of one fluid within another fluid.