The lowest bound states of the hydrogen negative ion and negative donor systems in a homogeneous magnetic field are investigated theoretically via a full configuration-interaction approach with an anisotropic Gaussian basis set. The broad magnetic field regime γ=8×10-4-4×103 is covered. Nonrelativistic total energies, electron detachment energies, and transition wavelengths are presented assuming an infinite nuclear mass. The binding mechanisms are discussed in detail. The accuracy for the energies is enhanced significantly compared to previously published data.