Starting from a multipole expansion of intramolecular Coulomb interactions, we present configuration interaction calculations of the molecular energy terms of the hole configurations (h(u)(+))(m), m=2-5, of C-60(m+) cations, of the electron configurations t(1u)(n), n=2-4, of the C-60(n-) anions, and of the exciton configurations (h(u)(+)t(1u)(-)), (h(u)(+)t(1g)(-)) of the neutral C-60 molecule. The ground state of C-60(2-) is either T-3(1g) or (1)A(g), depending on the energy separation between t(1g) and t(1u) levels. There are three close (similar to0.03 eV) low lying spin triplets T-3(1g), (3)G(g), T-3(2g) for C-60(2+), and three spin quartets T-4(1u), (4)G(u), T-4(2u) for C-60(3+), which can be subjected to the Jahn-Teller effect. The number of low lying nearly degenerate states is largest for m=3 holes. We have calculated the magnetic moments of the hole and electron configurations and found that they are independent of molecular orientation with respect to an external magnetic field. The coupling of spin and orbital momenta differs from the atomic case. We analyze the electronic dipolar transitions (t(1u))(2)-->t(1u)t(1g) and (t(1u))(3)-->(t(1u))(2)t(1g) for C-60(2-) and C-60(3-). Three optical absorption lines (T-3(1g)-->H-3(u), T-3(1u), (3)A(u)) are found for the ground level of C-60(2-) and only one line ((4)A(u-->)(4)T(1g)) for the ground state of C-60(3-). We compare our results with the experimental data for C-60(n-) in solutions and with earlier theoretical studies.