The energetics, geometrical and electronic structure, ionization processes, dynamics, and dissociation pathways of neutral and singly and doubly ionized water dimers are investigated with simulations employing the Born-Oppenheimer local-spin-density functional molecular dynamics (BO-LSD-MD) method. Vertical and adiabatic ionization potentials and dissociation energies and barriers are calculated for various dissociation channels of the singly and doubly ionized dimer. A new bound ground-state, (H2O)(2)(+)(a), with a hydrazine-like configuration, whose energy is lower by 0.22 eV than that of the disproportionated-ion isomer, (OH)(H3O)(+), is found for the singly charged dimer cation. A state with a similar geometry is found for a bound metastable state of the doubly ionized water dimer, whose dissociation into 2(H2O+) involves a barrier of similar to 0.68 eV. The dissociation pathways of the singly ionized dimer depend on the internal energy of the parent neutral and on the excitation energy, with the OH + H3O + channel dominating at low energies. Fission of the doubly ionized dimer into the H2O+ + H2O+ and OH+ + H3O+ channels can be influenced by the ionization process; direct double ionization of the neutral leads mainly to fission into the first channel, while sequential double ionization can lead to the other.