This paper studies the state-of-the-art classification techniques for electroencephalogram (EEG) signals. Fuzzy Functions Support Vector Classifier, Improved Fuzzy Functions Support Vector Classifier and a novel technique that has been designed by utilizing Particle Swarm Optimization and Radial Basis Function Networks (PSO-RBFN) have been studied. The classification performances of the techniques are compared on standard EEG datasets that are publicly available and used by brain-computer interface (BCI) researchers. In addition to the standard EEG datasets, the proposed classifier is also tested on non-EEG datasets for thorough comparison. Within the scope of this study, several data clustering algorithms such as Fuzzy C-means, K-means and PSO clustering algorithms are studied and their clustering performances on the same datasets are compared. The results show that PSO-RBFN might reach the classification performance of state-of-the art classifiers and might be a better alternative technique in the classification of EEG signals for real-time application. This has been demonstrated by implementing the proposed classifier in a real-time BCI application for a mobile robot control.