We analyzed the morphology of droplets of conductive liquids placed between two parallel plate electrodes as a function of the two control parameters electrode separation and applied voltage. Both electrodes were covered by thin insulating layers, as in conventional electrowetting experiments. Depending on the values of the control parameters, three different states of the system were found: stationary capillary bridges, stationary separated droplets, and periodic self-excited oscillations between both morphologies, which appear only above a certain threshold voltage. In the two stationary states, the morphology of the liquid is modified by the electric fields due to electrowetting and due to mutual electrostatic attraction, respectively. We determined a complete phase diagram within the two-dimensional phase space given by the control parameters. We discuss a model based on the interfacial and electrostatic contributions to the free energy. Numerical solutions of the model are in quantitative agreement with the phase boundaries found in the experiments. The dynamics in the oscillatory state are governed by electric charge relaxation and by contact angle hysteresis.