The magnetohydrodynamic (MHD) equations of incompressible viscous fluids with
finite electrical conductivity describe the motion of viscous electrically
conducting fluids in a magnetic field. In this paper, we find twelve families
of solutions of these equations by Xu's asymmetric and moving frame methods. A
family of singular solutions may reflect basic characteristics of vortices. The
other solutions are globally analytic with respect to the spacial variables. In
particular, Bernoulli equation and Wronskian determinants play important roles
in our approaches.