We present a search for point sources of high energy neutrinos using 3.8 yr of data recorded by AMANDA-II during 2000-2006. After reconstructing muon tracks and applying selection criteria designed to optimally retain neutrino-induced events originating in the northern sky, we arrive at a sample of 6595 candidate events, predominantly from atmospheric neutrinos with primary energy 100 GeV to 8 TeV. Our search of this sample reveals no indications of a neutrino point source. We place the most stringent limits to date on E-2 neutrino fluxes from points in the northern sky, with an average upper limit of E-2 Phi(nu mu)+nu(tau)<= 5.2x10(-11) TeV cm(-2) s(-1) on the sum of nu(mu) and nu(tau) fluxes, assumed equal, over the energy range from 1.9 TeV to 2.5 PeV.