The s-process should occur in all but the lower mass progenitor stars of planetary nebulae, and this should be reflected in the chemical composition of the gas that is expelled to create the current planetary nebula shell. Weak forbidden emission lines are expected from several s-process elements in these shells and have been searched for and in some cases detected in previous investigations. Here we extend these studies by combining very high signal-to-noise ratio echelle spectra of a sample of PNe with a critical analysis of the identification of the emission lines of Z>30 ions. Emission lines of Br, Kr, Xe, Rb, Ba, and Pb are detected with a reasonable degree of certainty in at least some of the objects studied here, and we also tentatively identify lines from Te and I, each in one object. The strengths of these lines indicate enhancement of s-process elements in the central star progenitors, and we determine the abundances of Br, Kr, and Xe, elements for which atomic data relevant for abundance determination have recently become available. As representative elements of the "light" and "heavy" s-process peaks, Kr and Xe exhibit similar enhancements over solar values, suggesting that PN progenitors experience substantial neutron exposure.