Doppler imaging is a technique for deriving resolved images of rapidly rotating stars from a detailed analysis of very high signal-to-noise high resolution spectral line profiles. An improved version of this technique is presented, which now uses principles of maximum entropy image reconstruction to invert the line profile information. The effects that noise, finite resolution, and uncertainties in the assumed stellar physics have on the resultant images were explored through various test simulations. The technique is found to be efficient, accurate, and robust at deriving images of certain classes of stars from realistic quality data. Doppler images are presented of two spotted late-type stars, the RS CVn-type star HR 1099, and the FK Com-type star HD 199178. Both stars show surprisingly similar spot distributions. In each case, there is a single large cool spot straddling the pole, and a number of small cool spots at low latitudes. We expect that the small low latitude spots on each star will migrate poleward to join the polar spot, and suspect that the observed long-lived polar spots are the result of the poleward migration and merging of many active region complexes. If true, the poleward migration of starspots suggests that magnetic activity on very rapidly rotating stars is qualitatively different than that seen on our Sun. We suggest that the observed rotational trigger velocity for the appearance of large spots on late-type stars marks the transition from solar-type boundary layer dynamos to distributed dynamos, which occur only in more rapidly rotating stars. The sizes, locations, and migrations of the spots, however, may be more a result of the convective flow patterns than of any dynamo action, since the spots are quite long-lived.