Speech Emotion Recognition (SER) is an interesting and difficult problem to handle. In this paper, we deal with it through the implementation of deep learning networks. We have designed and implemented six different deep learning networks, a Deep Belief Network (DBN), a simple deep neural network (SDNN), a LSTM network (LSTM), a LSTM network with the addition of an attention mechanism (LSTM-ATN), a Convolutional neural network (CNN), and a Convolutional neural network with the addition of an attention mechanism (CNN-ATN), having in mind, apart from solving the SER problem, to test the impact of attention mechanism to the results. Dropout and Batch Normalization techniques are also used to improve the generalization ability (prevention of overfitting) of the models as well as to speed up the training process. The Surrey Audio-Visual Expressed Emotion database (SAVEE), and the Ryerson Audio-Visual Database (RAVDESS) database were used for training and evaluation of our models. The results showed that networks with the addition of the attention mechanism did better than the others. Furthermore, they showed that CNN-ATN was the best among tested networks, achieving an accuracy of 74% for the SAVEE and 77% for the RAVDESS dataset, and exceeded existing state-of-the-art systems for the same datasets.