Rare isotopes such as 13C, 15N, and 17O have astrophysical significance, as their abundances with respect to the main isotope of each species (12C, 14N, and 16O, respectively) serve as effective tracers of stellar nucleosynthesis. While the Solar System values for these ratios are quite high (12C/13C ~ 89, 14N/15N ~ 435, 16O/17O ~ 2,632), observations of a plethora of chemical species and their 13C, 15N, and 17O-bearing variants in the planetary nebula (PN) K4-47 have yielded astonishingly high enrichment of the rare isotopes in this source, with 12C/13C = 2.0 ± 0.8; 14N/15N = 13.3 ± 6.5, and 16O/17O= 21.4 ± 10.3. Moreover, anomalously low 12C/13C ratios have now been detected in eight other PNe, including NGC 7293 (the Helix Nebula), M3-55, M3-28, M2-9 (the Butterfly Nebula), NGC 2440, and NGC 6720 (the Ring Nebula). The 12C/13C ratios for all eight sources were found to range between 1.0 ± 0.7 to 13.2 ± 4.9, with an average value of 3.7. These ratios are significantly lower than those seen in asymptotic giant branch (AGB) stars, which typically exhibit 12C/13C ~ 25–90. Together with the extreme bipolar/multipolar morphologies exhibited by all of these nebulae, the high enrichment of 13C suggests that an explosive process involving proton capture took place at some point in the transition between the AGB and PN phases. Details of the observations of these isotopically-substituted species and their analysis will be presented, along with the implications for our understanding of stellar nucleosynthesis in the late AGB stage.