Memory effects in single nanocrystal fluorescence blinking are investigated as a function of the on-state kinetics for CdSe/ZnS quantum dots and CdSe nanorods. The on-state duration probability distributions for single nanocrystal blinking traces are characterized by an inverse power law, which crosses over to exponential decay for long on-state durations. The correlations of subsequent on-state durations (R-log,R-on) are found to decrease for nanocrystals that display earlier crossover times and smaller power law coefficients. Specifically, R-log,R-on increases from 0.14 +/- 0.02 to a saturation value of 0.44 +/- 0.01 for nanocrystals with average crossover times of similar to 100 ms to more than 5.0 s, respectively. The results represent the first link between memory effects and blinking kinetics and are interpreted in the framework of two competing charge trapping mechanisms. A slow fluctuation-based trapping mechanism leads to power-law-distributed on durations and significant memory effects; however, the additional contribution of an ionization induced trapping pathway is found to induce crossover to exponential decay and decreased memory. Monte Carlo simulations of nanocrystal blinking based on the two trapping mechanisms reproduce the experimental results, suggesting that the power law component and the memory effects correlate with a fluctuation-based mechanism. This effect is found to be universal, occurring for two nanocrystal morphologies and in blinking data measured using a wide range of continuous and pulsed excitation conditions.