This work considers the problem of utilizing electroencephalographic signals for use in systems designed for monitoring and enhancing the performance of aircraft pilots. Systems with such capabilities are generally referred to as cognitive cockpits. This article provides a description of the potential that is carried by such systems, especially in terms of increasing flight safety. Additionally, a neuropsychological background of the problem is presented. Conducted research was focused mainly on the problem of discrimination between states of brain activity related to idle but focused anticipation of visual cue and reaction to it. Especially, a problem of selecting a proper classification algorithm for such problems is being examined. For that purpose an experiment involving 10 subjects was planned and conducted. Experimental electroencephalographic data was acquired using an Emotiv EPOC+ headset. Proposed methodology involved use of a popular method in biomedical signal processing, the Common Spatial Pattern, extraction of bandpower features, and an extensive test of different classification algorithms, such as Linear Discriminant Analysis, k-nearest neighbors, and Support Vector Machines with linear and radial basis function kernels, Random Forests, and Artificial Neural Networks.