Self-resonant wireless power transfer (WPT) system can achieve high reliability due to the elimination of physical compensation capacitors. Planar coils that have parasitic capacitance between adjacent layers are ideal candidates for self-resonant WPT systems, and the coil geometry has a significant influence on the performance of WPT system. This paper studies and compares three typical coil geometries, namely circular, square, and hexagonal coils. The mutual inductance, coupling coefficient, magnetic field of coils, ac resistance, output power, and efficiency have been calculated and compared using finite element method. Simulation results show that hexagonal planar coil can transfer the largest power and has the highest efficiency.