A general framework for goal-oriented a posteriori error estimation for finite volume methods is developed. The framework does not rely on recasting finite volume methods as special cases of finite element methods, but instead directly determines error estimators from the discretized finite volume equations. Thus, the framework can be applied to arbitrary finite volume methods. It also provides the proper functional settings to address well-posedness issues for the primal and adjoint problems. Numerical results are presented to illustrate the validity and effectiveness of the a posteriori error estimates and their applicability to adaptive mesh refinement.