Given the recent increase of interest in introducing new vehicle types and missions into the National Airspace System, a transition towards a more autonomous air traffic control system is required in order to enable and handle increased density and complexity. This paper presents an exploratory effort of the needed autonomous capabilities by exploring supervised learning techniques in the context of aircraft trajectories. In particular, it focuses on the application of machine learning algorithms and neural network models to a runway recognition trajectory-classification study. It investigates the applicability and effectiveness of various classifiers using datasets containing trajectory records for a month of air traffic. A feature importance and sensitivity analysis are conducted to challenge the chosen time-based datasets and the ten selected features. The study demonstrates that classification accuracy levels of 90% and above can be reached in less than 40 seconds of training for most machine learning classifiers when one track data point, described by the ten selected features at a particular time step, per trajectory is used as input. It also shows that neural network models can achieve similar accuracy levels but at higher training time costs.