Let textbf{u} be a moment functional associated with the Hermite, Laguerre, or Jacobi classical orthogonal polynomials. We study approximation by polynomials in H^r(textbf{u}), the Sobolev space consisting of functions whose derivatives of consecutive orders up to r belong to the L^2 space associated with textbf{u}. This requires the simultaneous approximation of a function f and its consecutive derivatives up to order Nleqslant r. We explicitly construct orthogonal polynomials that achieve such simultaneous approximation and provide error estimates in terms of E_n(f^{(r)}), the error of best approximation of f^{(r)} in L^{2}(textbf{u}).