Heavy elements, those produced by neutron-capture reactions, have traditionally shown no star-to-star dispersion in all but a handful of metal-poor globular clusters (GCs). Recent detections of low [Pb/Eu] ratios or upper limits in several metal-poor GCs indicate that the heavy elements in these GCs were produced exclusively by an r-process. Reexamining GC heavy element abundances from the literature, we find unmistakable correlations between the [La/Fe] and [Eu/Fe] ratios in 4 metal-poor GCs (M5, M15, M92, and NGC 3201), only 2 of which were known previously. This indicates that the total r-process abundances vary star-to-star (by factors of 2-6) relative to Fe within each GC. We also identify potential dispersion in two other GCs (M3 and M13). Several GCs (M12, M80, and NGC 6752) show no evidence of r-process dispersion. The r-process dispersion is not correlated with the well-known light element dispersion, indicating it was present in the gas throughout the duration of star formation. The observations available at present suggest that star-to-star r-process dispersion within metal-poor GCs may be a common but not ubiquitous phenomenon that is neither predicted by nor accounted for in current models of GC formation and evolution.