Brain Computer interfaces (BCI) has immense potentials to improve human lifestyle including that of the disabled. BCI has possible applications in the next generation human-computer, human-robot and prosthetic/assistive devices for rehabilitation. The dataset used for this study has been obtained from the BCI competition-II 2003 databank provided by the University of Technology, Graz. After pre-processing of the signals from their electrodes (C3 & C4), the wavelet coefficients, Power Spectral Density of the alpha and the central beta band and the average power of the respective bands have been employed as features for classification. This paper presents a comparative study of different classification methods including linear discriminant analysis (LDA), Quadratic discriminant analysis (QDA), k-nearest neighbor (KNN) algorithm, linear support vector machine (SVM), radial basis function (RBF) SVM and naive Bayesian classifiers algorithms in differentiating the raw EEG data obtained, into their associative left/right hand movements. Performance of left/right hand classification is studied using both original features and reduced features. The feature reduction here has been performed using Principal component Analysis (PCA). It is as observed that RBF kernelised SVM classifier indicates the highest performance accuracy of 82.14% with both original and reduced feature set. However, experimental results further envisage that all the other classification techniques provide better classification accuracy for reduced data set in comparison to the original data. It is also noted that the KNN classifier improves the classification accuracy by 5% when reduced features are used instead of the original.