FNAL E866/NuSea has made a number of measurements of J /ψ and ψ′ production by 800 GeV protons on fixed targets of Be, Fe and W. Preliminary results are presented and discussed in the context of nuclear effects such as energy loss and multiple scattering of the partons, absorption of the produced cc pairs, and shadowing. Production mechanisms involving color-singlet or color-octet states for the cc pair which eventually forms a J /ψ or ψ′ have implications on the strength of absorption in the nucleus. These nuclear dependence studies are critical in furthering our understanding of these processes towards future measurements at RHIC and the LHC, where J /ψ suppression is predicted to be an important signature of the creation of quark-gluon plasma in heavy-ion collisions.