This paper proposes genetic algorithms (GAs) for path planning and trajectory planning of an autonomous mobile robot. Our GA-based approach has an advantage of adaptivity such that the GAs work even if an environment is time-varying or unknown. Therefore, it is suitable for both off-line and on-line motion planning. We first presents a GA for path planning in a 2D terrain. Simulation results on the performance and adaptivity of the GA on randomly generated terrains are shown. Then, we discuss an extension of the GA for solving both path planning and trajectory planning simultaneously.