We experimentally investigated the effect of post-growth annealing on the morphological, structural, and electrophysical parameters of nanocrystalline ZnO films fabricated by pulsed laser deposition. The influence of post-growth annealing modes on the electroforming voltage and the resistive switching effect in ZnO nanocrystalline films is investigated. We demonstrated that nanocrystalline zinc oxide films, fabricated at certain regimes, show the electroforming-free resistive switching. It was shown, that the forming-free nanocrystalline ZnO film demonstrated a resistive switching effect and switched at a voltage 1.9 ± 0.2 V from 62.42 ± 6.47 (RHRS) to 0.83 ± 0.06 kΩ (RLRS). The influence of ZnO surface morphology on the resistive switching effect is experimentally investigated. It was shown, that the ZnO nanocrystalline film exhibits a stable resistive switching effect, which is weakly dependent on its nanoscale structure. The influence of technological parameters on the resistive switching effect in a forming-free ZnO nanocrystalline film is investigated. The results can be used for fabrication of new-generation micro- and nanoelectronics elements, including random resistive memory (ReRAM) elements for neuromorphic structures based on forming-free ZnO nanocrystalline films.