Classical limit of quantum mechanics

I have heard that one can recover classical mechanics from quantum mechanics in the limit the $\hbar$ goes to zero. How can this be done? (Ideally, I would love to see something like: as $\hbar$ goes to zero, the position wavefunction reduces to a delta function and that the Schrodinger equation/Feynman path integral reduces to the Newtonian/Lagrangian/Hamiltonian equations of motion.)