Power system operators obtain information about an electrical grid's current condition using available tools in control centers. These tools employ simple algorithms for data analysis and processing to expedite decision making. We propose to use Deep Learning algorithms to provide more information about the power system's operating condition without loss in computational performance. This work performs a comparison between several Deep Learning algorithms for time series-based classification of power system small-signal stability, which can be applied to both PMU data or synthetic measurements from simulations. In particular, several case studies are performed using line current and bus voltage data as input for the proposed algorithms. To find the best method for the classification task, the following neural network (NN) architectures are studied: a multi-layer perceptron, a fully-convolutional NN, an inception network, a time convolutional NN, and a multi-channel deep convolutional NN. Training and testing data sets were obtained from the IEEE 9 bus system by performing dynamic simulations subjected to a vast array of operating conditions (i.e., different power flow solutions, and contingencies). The computational time of the implemented algorithms is measured. The multi-channel deep convolutional NN shown the best performance in most of the reviewed cases.