Electronic and geometrical structures of the homonuclear 3d metal dimers M-2 (from Sc-2 to Zn-2) as well as their M-2(-) anions and M-2(+) cations are computed using density functional theory with six generalized gradient approximations for the exchange-correlation potential. The neutral ground states are assigned as follows: Sc-2 ((5)Sigma(u)(-)), Ti-2 ((3)Delta(g)), V-2 ((3)Sigma(g)(-)), Cr-2 ((1)Sigma(+)), Mn-2 ((11)Pi(u)), Fe-2 ((7)Delta(u)), Co-2 ((5)Delta(g)), Ni-2 ((3)Sigma(g)(-)), Cu-2 ((1)Sigma(g)(+)), and Zn-2 ((1)Sigma(g)(+)). The anions are assigned as follows: Sc-2(-) ((4)Sigma(g)(-)), Ti-2(-) ((4)Delta(u)), V-2(-) ((4)Sigma(+)), Mn-2(-) ((10)Sigma(g)(-)), Fe-2(-) ((8)Delta(g)), Co-2(-) ((6)Delta(u)), Ni-2(-) ((4)Sigma(u)(-)), and Cu-2(-) ((2)Sigma(u)(+)) (Zn-2(-) is unbound). The cations ground states are: Sc-2(+) ((4)Sigma(g)(-)), Ti-2(+) ((2)Delta(g)), V-2(+) ((4)Sigma(g)(-)), Cr-2(+) ((2)Sigma(+)), Mn-2(+) ((10)Pi(u)), Fe-2(+) ((8)Delta(u)), Co-2(+) ((6)Gamma(g)), Ni-2(+) ((4)Delta(g)), Cu-2(+) ((2)Sigma(g)(+)), and Zn-2(+) ((2)Sigma(u)(+)). A natural bond (NBO) analysis is used to obtain the chemical bonding patterns in the neutral and charged dimers. The results of the NBO analysis allow us to explain the changes in the ground-state spin multiplicities and spatial symmetries when moving along the neutral and ionic series. Consistent changes in the chemical bonding patterns of the neutral and charged dimers lend further support to our assignment of the ground states in the M-2(-) and M-2(+) series. Our calculated adiabatic electron affinities and ionization energies are in good agreement with experiment.