Numerical methods are employed to examine the work, electric power input, and efficiency of electrokinetic pumps at a condition corresponding to maximum pump work. These analyses employ the full Poisson-Boltzmann equations and account for both convective and conductive electric currents, including surface conductance. We find that efficiencies at this condition of maximum work depend on three dimensionless parameters, the normalized zeta potential, normalized Debye layer thickness, and a fluid property termed the Levine number indicating the nominal ratio of convective to conductive electric currents. Efficiencies at maximum work exhibit a maximum for an optimum Debye layer thickness when the zeta potential and Levine number are fixed. This maximum efficiency increases with the square of the zeta potential when the zeta potential is small, but reaches a plateau as the zeta potential becomes large. The maximum efficiency in this latter regime is thus independent of the zeta potential and depends only on the Levine number. Simple analytical expressions describing this maximum efficiency in terms of the Levine number are provided. Geometries of a circular tube and planar channel are examined.