Discrimination of eye movements and visual states is a flourishing field of research and there is an urgent need for non-manual EEG-based wheelchair control and navigation systems. This paper presents a novel system that utilizes a brain–computer interface (BCI) to capture electroencephalographic (EEG) signals from human subjects while eye movement and subsequently classify them into six categories by applying a random forests (RF) classification algorithm. RF is an ensemble learning method that constructs a series of decision trees where each tree gives a class prediction, and the class with the highest number of class predictions becomes the model’s prediction. The categories of the proposed random forests brain–computer interface (RF-BCI) are defined according to the position of the subject’s eyes: open, closed, left, right, up, and down. The purpose of RF-BCI is to be utilized as an EEG-based control system for driving an electromechanical wheelchair (rehabilitation device). The proposed approach has been tested using a dataset containing 219 records taken from 10 different patients. The BCI implemented the EPOC Flex head cap system, which includes 32 saline felt sensors for capturing the subjects’ EEG signals. Each sensor caught four different brain waves (delta, theta, alpha, and beta) per second. Then, these signals were split in 4-second windows resulting in 512 samples per record and the band energy was extracted for each EEG rhythm. The proposed system was compared with naïve Bayes, Bayes Network, k-nearest neighbors (K-NN), multilayer perceptron (MLP), support vector machine (SVM), J48-C4.5 decision tree, and Bagging classification algorithms. The experimental results showed that the RF algorithm outperformed compared to the other approaches and high levels of accuracy (85.39%) for a 6-class classification are obtained. This method exploits high spatial information acquired from the Emotiv EPOC Flex wearable EEG recording device and examines successfully the potential of this device to be used for BCI wheelchair technology.