Accurate and efficient inference and prediction are important elements in intelligent systems. Knowing in advance the behaviour of an entity, such as the price of a product in the future, the weather in the next few days or the position of an object in the near future, is important for several applications like stock market, weather forecasting, robotics and more recently for autonomous vehicles. The aim of this work is to investigate and develop a novel approach for predicting the path of moving objects such as pedestrians and vehicles in the context of ego-cameras, like those mounted on a vehicle or a person. Due to the sequential nature of the data presented in paths, Recurrent Neural Networks (RNNs) are exploited, specifically Long Short-Term Memory Networks (LSTMs), due to their ability to process this type of data. LSTMs have the limitation of only predicting a single path per tracklet. Path prediction requires predicting with a level of uncertainty. Predicting multiple future paths instead of a single one is therefore a more realistic manner of approaching this task. In this work, predicting a set of future paths with associated uncertainty was achieved by combining LSTMs and MDNs. One of the objectives of this work is to include more information than simple position in the path prediction task, such as velocity of the ego vehicle and contextual information of the surroundings. Though the main interest of this work is on egocentric cameras experiments were also conducted using fixed cameras for a surveillance perspective. Two public datasets were used: KITTI and CityFlow. In summary, this thesis extends moving object path prediction methods in the context of traffic scenes for objects such as pedestrians, vehicles, cyclists.