Planar electron optical systems, with emphasis on planar deflectors, were investigated by computer simulation in three dimensions (3D). The simulations were carried out using a computer program based on the surface charge density method, with a coordinate system to assist meshing of boundary elements. Simulation of electron trajectories in 3D offers the possibility to see the final spot on an anode plane, helping to optimize the electron optical design. Three types of planar deflectors, split ring, microstrip, and horizontal bars were investigated to demonstrate their capability of deflecting electrons from a field emitter or a field emitter array. Some applications for these planar deflection systems have been suggested. Simple to fabricate and easy to be integrated with a field emitter are the biggest advantages for these planar electron optical systems. With the assistance of computer simulation, a better performance from these planar systems can also be achieved.