Analyzing the noise in the momentum profiles of single realizations of one-dimensional Bose gases, we present the experimental measurement of the full momentum-space density correlations δnpδn p , which are related to the two-body momentum correlation function. Our data span the weakly interacting region of the phase diagram, going from the the ideal Bose gas regime to the qua-sicondensate regime. We show experimentally that the bunching phenomenon, which manifests itself as super-Poissonian local fluctuations in momentum space, is present in all regimes. The quasicon-densate regime is however characterized by the presence of negative correlations between different momenta, in contrast to Bogolyubov theory for Bose condensates, predicting positive correlations between opposite momenta. Our data are in good agreement with ab-initio calculations.