The formation of the negative hydrogen ion (H-) in collisions between a positive ion and a neutral atomic or molecular target is studied experimentally at impact energies of a few keV. The doubly-differential cross sections for H- formation are measured as a function of the kinetic energy and emission angle for the collision systems OH+ + Ar and O+ + H2O à 412 eV/a.m.u. These H- ions can be emitted at high energies (keV) in hard quasi-elastic two-body collisions involving a large momentum transfer to the H center. However, H- ions are preferentially emitted at low energy (eV) due to soft many-body (>2) collisions resulting in a low momentum transfer. The formation of H- ions by electron capture follows excitation or ionization of the molecule. The molecular fragmentation dynamics is modeled to simulate the emission of H- ions. The overall good agreement between the simulation and the experiment leads to the understanding of most of the experimental observations.