Photoconductivity in nanocrystal films has been previously characterized, but memory effects have received little attention despite their importance for device applications. We show that the magnitude and temperature dependence of the photocurrent in CdSe/ZnS core-shell nanocrystal arrays depends on the illumination and electric field history. Changes in photoconductivity occur on a few-hour timescale, and subband gap illumination of nanocrystals prior to measurements modifies the photocurrent more than band gap illumination. The observed effects can be explained by charge traps within the band gap that are filled or emptied, which may alter nonradiative recombination processes and affect photocurrent.