The fluctuations of natural populations have deep impact on important ecological issues, such as pest outbreaks, fisheries or the formation of harmful algal blooms (HABs). However, consensus on the appropriate descriptor of such fluctuations is still lacking. Here, using 16 to 20 years of weekly data on marine microbial population abundance comprising more than 200 species, we analysed the distribution of the population fluctuations. We found that population fluctuations of all groups and in 12 out of 17 species were not Gaussian (D’Agostino test p < 0.05) but instead were adequately described by Levy-stable distributions (LSD). Consistent with ecological theories, the LSD characteristic parameter (α) characterizes as highly volatile those groups known to form HABs, such as dinoflagellates (α= 1.48), and as lowly volatile, nanoflagellates (α= 1.92), a group which can be subjected to predatory control. Moreover, zooplankton groups composed of species with sexual reproduction and complex life cycles such as crustacean and Appendicullaria also showed departures from Gaussian population fluctuations and adequate fits to LSD. Our results suggest that heavy-tailed population fluctuations are widespread, implying that extreme population fluctuations are more likely than previously expected, a fact that has important consequences for the predictability of population outbreaks.