The technology developed for micropatterning the electric surface charge to be negative, positive or neutral enables the realization of complex liquid flows in simple microchannels. A commercial CFD code is utilized to numerically simulate a variety of electrokinetically-generated liquid flows in a straight and uniform microchannel due to non-uniform surface charge distribution under an externally applied, steady electric field. We present design methodologies to electrokinetically drive vortical flows in any desired direction. In particular, we investigate surface charge patterns required to generate single or multi, co-rotating or counter-rotating, in-plane or out-of-plane vortices. Finally, in view of its potential application to microscale mixing, we discuss a surface charge pattern that can give rise to streamwise vorticity.