The neutrino production rates for a spallation neutron source with proton beams in the energy range 650<Tp<2200 MeV are calculated to an estimated accuracy of 25%. The target geometries used are based on the tantalum and mercury targets proposed for the European Spallation Source. Results for νμ, νe, and ν rates due to π+ and μ+ decay at rest, and for νμ rates from π+ decay in flight, are presented in terms of neutrinos per proton. Production rates for decay at rest from a tantalum target are calculated to be (ν p-1) = 0.075 at Tp = 1000 MeV, and 0.327 at 2200 MeV. For a neutrino detector located 20 m from a tantalum target, and at 0° to a 1500 MeV proton beam, the integrated flux of νμ above 150 MeV from π+ decay in flight is 3.0 × 105 cm-2 s-1. Backgrounds of νe, from the π- decay-in-flight and μ- decay-at-rest chain, vary from 0.05% to 0.09% of the νe flux.