This paper presents a review and a computational comparison of various
stabilization techniques developed to diminish spurious oscillations in finite element solutions of scalar stationary convection-diffusion equations. All these methods are defined by enriching the popular SUPG discretization by additional stabilization terms. Although some of the methods can substantially enhance the quality of the discrete solutions in comparison to the SUPG method, any of the methods can fail in very simple situations and hence none of the methods can be regarded as reliable. We also present results obtained using the improved Mizukami-Hughes method which is often superior to techniques based on the SUPG method.