New gauge bosons with Standard Model-like couplings to leptons are constrained by collider searches to be heavier than approximately ~1 TeV. A Z' boson with suppressed couplings to leptons, however, could be much lighter and possess substantial couplings to Standard Model quarks. In this article, we consider a new leptophobic Z' gauge boson as a simple and well motivated extension of the Standard Model, and discuss several of its possible signatures at the Tevatron. We find that three of the recent anomalies reported from the Tevatron - in particular the top-quark forward-backward asymmetry and excesses in the 3b and W + 2 jets final states - could be explained by a new Z' with a mass of approximately 150 GeV, relatively large couplings to quarks, and suppressed couplings to electrons and muons. Moreover, we find that such a particle could also mediate the interactions of dark matter, leading to potentially interesting implications for direct detection experiments.