We consider Non-Standard neutrino Interactions (NSI), described by four-fermion operators of the form ((nu) over bar (alpha)gammanu(beta)) ((f) over bar gammaf), where f is an electron or first generation quark. We assume these operators are generated at dimension greater than or equal to 8, so the related vertices involving charged leptons, obtained by an SU(2) transformation nu(delta)-->e(delta), do not appear at tree level. These related vertices necessarily arise at one loop, via W exchange. We catalogue current constraints from sin(2)theta(W) measurements in neutrino scattering, from atmospheric neutrino observations, from LEP, and from bounds on the related charged lepton operators. We estimate future bounds from comparing KamLAND and solar neutrino data, and from measuring sin(2)theta(w) at the near detector of a neutrino factory. Operators constructed with nu(mu) and nu(e) should not confuse the determination of oscillation parameters at a nufactory, because the processes we consider are more sensitive than oscillations at the far detector. For operators involving nu(tau), we estimate similar sensitivities at the near and far detector.