Wind energy is a valuable source of electric power as its motion can be converted into mechanical energy, and ultimately electricity. The significant variability of wind speed calls for highly robust estimation methods. In this study, the mechanical power of wind turbines (WTs) is successfully estimated using input variables such as wind speed, angular speed of WT rotor, blade pitch, and power coefficient (Cp). The feed-forward backpropagation neural networks (FFBPNNs) and recurrent neural networks (RNNs) are incorporated to perform the estimations of wind turbine output power. The estimations are performed based on diverse parameters including the number of hidden layers, learning rates, and activation functions. The networks are trained using a scaled conjugate gradient (SCG) algorithm and evaluated in terms of the root mean square error (RMSE) and mean absolute percentage error (MAPE) indices. FFBPNN shows better results in terms of RMSE (0.49%) and MAPE (1.33%) using two and three hidden layers, respectively. The study indicates the significance of optimal selection of input parameters and effects of changing several hidden layers, activation functions, and learning rates to achieve the best performance of FFBPNN and RNN.