Balancing electricity production and distribution remains a central challenge in modern energy systems, especially with the increasing penetration of renewable sources that introduce variability and uncertainty. In this context, accurate forecasting of electricity demand is essential for grid stability and operational efficiency. This study addresses the problem of hourly electricity demand forecasting in Italy using recurrent neural networks (RNNs), particularly long short-term memory (LSTM) models, which are designed to capture complex temporal dependencies in time series data. Utilizing real consumption data from Terna-Rete Elettrica Nazionale S.p.A.-for the years 2022 and 2023, we developed and tested an LSTM model capable of predicting national hourly demand with Root Mean Squared Error (RMSE) consistently below 2%. The model's forecasts show strong agreement with official data provided by Terna, accurately capturing demand peaks and seasonal trends over both short- and medium-term horizons. In addition to evaluating predictive performance, this work proposes a reproducible methodology applicable to other national contexts or similar forecasting problems. Our findings suggest that, while data-driven models offer robust and replicable results, further improvements may require the integration of system-specific knowledge to address persistent limitations in forecasting extreme events or structural anomalies.