The Tangni landslide in Chamoli, India, has experienced several landslide incidents in the recent past. Due to the fatalities and injuries caused, it is essential to predict slope movements at this site. A recent approach to predicting slope movements is via machine-learning algorithms. In machine learning literature, recurrent neural networks (simple LSTMs, stacked LSTMs, bidirectional LSTMs, convolutional LSTMs, CNN-LSTMs, and encoder–decoder LSTMs) and non-recurrent neural networks (multilayer perceptrons) have been proposed. However, evaluating recurrent and non-recurrent neural networks for real-world slope movements prediction has been less explored. This research’s primary objective is to develop and evaluate novel recurrent and non-recurrent neural network algorithms in their ability to predict slope movements. We used two years’ weekly data of slope movements from the Tangni landslide site in Chamoli, India. Different recurrent and non-recurrent neural networks were calibrated on the training data and then predicted the test data. Different hyperparameters (epochs; packet shuffle; look-back period; the number of nodes per layer; and the number of layers) were calibrated to training data. Later, the developed models were evaluated on test data. Results revealed that, during training, the recurrent stacked LSTMs and bidirectional LSTMs performed the best and second-best, respectively, compared to other recurrent and non-recurrent neural networks. However, during the test, the recurrent CNN-LSTMs and simple LSTMs performed best and second best, respectively, compared to other recurrent and non-recurrent neural networks. We discuss the implications of our results for predicting slope movements at real-world landslide sites.