We give a complete characterization on which finitely generated subgroups of finitely generated 3-manifold groups are separable. Our characterization generalizes Liu's spirality character on \pi_1-injective immersed surface subgroups of closed 3-manifold groups. A consequence of our characterization is that, for any compact, orientable, irreducible and boundary-irreducible 3-manifold M with nontrivial torus decomposition, \pi_1(M) is LERF if and only if for any two adjacent pieces in the torus decomposition of M, at least one of them has a boundary component with genus at least 2.