Given the constantly changing market situation for electricity prices, driven by shifts in the energy mix, regulatory reforms, and broader socio-economic factors, it is necessary to reassess the understanding of price forecasting periodically. Traditional statistical methods may struggle when faced with heightened volatility, nonlinear dependencies, and rapidly changing input features. In contrast, machine learning models, particularly Artificial Neural Networks (ANNs), can adapt more effectively to complex, non-stationary patterns in price time series. In this study, six distinct artificial neural network (ANN) architectures were developed and trained using eight years of historical Polish Day-Ahead Market electricity price data (2016–2024). Four of these were plain deep learning models: a Multilayer Perceptron (MLP), a Convolutional Neural Network (CNN), a Long Short-Term Memory (LSTM) model, and a Gated Recurrent Unit (GRU) model. Two others were hybrid models combining convolutional layers with recurrent layers. The hybrid architectures, namely CNN+LSTM and CNN+GRU, were designed to leverage the capacity of CNN to automatically extract features from narrower sliding windows of past prices and the LSTM/GRU layers’ ability to capture long-term temporal dependencies. The models’ performances were evaluated using three metrics: Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and the coefficient of determination (R2). The top-performing CNN+LSTM achieved an MAE of 75.21 PLN/MWh, an RMSE of 103.64 PLN/MWh, and an R2 of 0.59. Results were also compared against several models previously reported in the literature. These results may be used to improve price forecasting by indicating the optimal pathways for building forecasting models and, in extension, lead to more efficient power system planning.