We experimentally observed oscillatory motion of water droplets in microfluidic systems with coplanar microelectrodes under imposed DC electric fields. Two-electrode arrangement with no bipolar electrode and eight-electrode arrangement with six bipolar microelectrodes were investigated. Kerosene was used as the continuous phase. We studied the dependences of the oscillation frequency on the electric field intensity and ionic strength of the water phase. We found that the electric field dependence is strongly nonlinear and discussed possible reasons of this phenomenon, e.g., the droplet deformation at electrode edges that affects the charge transfer between the electrode and droplet or the interplay between the Coulomb force on free charge and the dielectrophoretic force. Our experiments further revealed that the oscillation frequency decreases with growing salt concentration in the two-electrode arrangement, but increases in the eight-electrode arrangement, which was attributed to surface tension related processes and electrochemical processes on the bipolar electrodes. Finally, we analyzed the effects of the electric field on the oscillatory motion by means of a simplified mathematical model. It was shown that the electric force imposed on the droplet charge is the key factor to induce the oscillations and the dielectrophoretic force significantly contributes to the momentum transfer at the electrode edges. For the same electric field strength, the model is able to predict the same oscillation frequency as that observed in the experiments.