The blinking behavior of perylene diïmide molecules is investigated at the single-molecule level. We observe long-time scale blinking of individual multi-chromophoric complexes embedded in a poly(methylmethacrylate) matrix, as well as for the monomeric dye absorbed on a glass substrate at ambient conditions. In both these different systems, the blinking of single molecules is found to obey analogous power-law statistics for both the on and off periods. The observed range for single-molecular power-law blinking extends over the full experimental time window, covering four orders of magnitude in time and six orders of magnitude in probability density. From molecule to molecule, we observe a large spread in off-time power-law exponents. The distributions of off-exponents in both systems are markedly different whereas both on-exponent distributions appear similar. Our results are consistent with models that ascribe the power-law behavior to charge separation and (environment-dependent) recombination by electron tunneling to a dynamic distribution of charge acceptors. As a consequence of power-law statistics, single molecule properties like the total number of emitted photons display non-ergodicity.