We investigate the ballistic motion of electrons and holes in III-V semiconductor quantum wells with spin-orbit coupling and a homogeneous in-plane electric field. As a result of a nonperturbative treatment of both of these influences, particle wave packets undergo a pronounced side jump perpendicular to the field direction. For wave packets of sufficient width the amplitude of this motion can be estimated analytically and increases with decreasing field strength. We discuss the scaling behavior of the effect and some of its experimental implications.