We study the numerical solution of optimal control problems associated with the two-dimensional viscous incompressible flows which are governed by the Navier-Stokes equations. Although the techniques apply to more general settings, the presentation is confined to the objectives of minimizing the vorticity in the steady-state case with distributed controls and tracking the velocity field in the nonstationary case with piecewise distributed controls. In the steady-state case, we develop a systematic way to use the Lagrange multiplier rules to derive an optimality system of equations from which an optimal solution can be computed; finite element methods are used to find approximate solutions for the optimality system of equations. In the time-dependent case, a piecewise-in-time optimal control approach is proposed and the fully discrete approximation algorithm for solving the piecewise optimal control problem is defined. Numrical results are presented for both the steady-state and time-dependent optimal control problems.