The large, faint, generally circular, and limb-brightened nebular structures (called "halos") surrounding some planetary nebulae (PN) are explored using deep CCD images of NGC 40, 650-1, 1535, 2392, 6210, 6543, 6720, 6803, 6804, 6826, 6853, 6891, 6894, 7009, 7662, IC 1454, 3568, 4593, Abell 1, 2, 3, and BD +30-degrees-3639. New halos have been discovered in a few objects (IC 1454, 4593, and possibly NGC 40, 6210, and 6803), and known halos have been mapped in detail in several PN (e.g., NGC 6543, 6720, 6826, 6853 and 7662). Surprisingly, our deep search does not reveal similar large and faint halos in NGC 1535, 2392, 6894, 7009, and IC 3568-PN whose inner regions are morphologically similar to others with easily observable halos. Halos are believed to represent early episodes of mass ejection from the central star. The detected halos are all limb-brightened, characterized by radii of almost-equal-to 0.3-0.5 pc, and are more circular than the PN which they surround. All of the newly detected halos as well as those previously identified have the emission measure distributions expected after almost-equal-to 10(4) yr if hydrodynamic effects control the evolution of the mass distribution of ejecta from the nucleus, as described by Frank, Balick, & Riley in 1990.