A model to study the dynamics of colloidal particles in nonuniform electric fields is proposed. For an isolated sphere, the conditions and threshold for sustained (Quincke) rotation in a linear direct current (dc) field are determined. Particle dynamics becomes more complex with increasing electric field strength, changing from steady spinning around the particle center to time-dependent orbiting motion around the minimum field location. Pairs of particles exhibit intricate trajectories, which are a combination of translation, due to dielectrophoresis, and rotation, due to the Quincke effect. Our model provides a basis to study the collective dynamics of many particles in a general electric field.