By large-scale quantum Monte Carlo simulations we show that grain boundaries in 4He crystals are generically superfluid at low temperature, with a transition temperature of the order of ∼0.5  K at the melting pressure; nonsuperfluid grain boundaries are found only for special orientations of the grains. We also find that close vicinity to the melting line is not a necessary condition for superfluid grain boundaries, and a grain boundary in direct contact with the superfluid liquid at the melting curve is found to be mechanically stable and the grain-boundary superfluidity observed by Sasaki et al. [Science 313, 1098 (2006)] is not just a crack filled with superfluid.