The changing climate is a concern with regard to sustainable water resources. Projections of the runoff in future climate conditions are needed for long-term planning of water resources and flood protection. In this study, we evaluate the possible climate change impacts on the runoff regime in eight selected basins located in the whole territory of Slovakia. The projected runoff in the basins studied for the reference period (1981–2010) and three future time horizons (2011–2040, 2041–2070, and 2071–2100) was simulated using the HBV (Hydrologiska Byråns Vattenbalansavdelning) bucket-type model (the TUW (Technische Universität Wien) model). A calibration strategy based on the selection of the most suitable decade in the observation period for the parameterization of the model was applied. The model was first calibrated using observations, and then was driven by the precipitation and air temperatures projected by the KNMI (Koninklijk Nederlands Meteorologisch Instituut) and MPI (Max Planck Institute) regional climate models (RCM) under the A1B emission scenario. The model’s performance metrics and a visual inspection showed that the simulated runoff using downscaled inputs from both RCM models for the reference period represents the simulated hydrological regimes well. An evaluation of the future, which was performed by considering the representative climate change scenarios, indicated that changes in the long-term runoff’s seasonality and extremality could be expected in the future. In the winter months, the runoff should increase, and decrease in the summer months compared to the reference period. The maximum annual daily runoff could be more extreme for the later time horizons (according to the KNMI scenario for 2071–2100). The results from this study could be useful for policymakers and river basin authorities for the optimum planning and management of water resources under a changing climate.