We use intense femtosecond laser pulses to multiply ionize and directly image the structures of N(2)Ar, O(2)Ar, and O(2)Xe dimers by coincidently measuring the momenta of the fragment ions. All these dimers are found to have an equilibrium T-shaped structure in which the bond of the diatomic molecule is perpendicular to the dimer axis. The equilibrium distance between the rare-gas atom and the center-of-mass of the diatomic molecule is estimated to be R(N2-Ar) ~ 3.86 Å, R(O2-Ar) ~ 3.65 Å, and R(O2-Xe) ~ 4.07 Å, respectively. For the T-shaped N(2)Ar dimer, both sequential and direct triple-ionization-induced three-body breakups are observed. In contrast to N(2)Ar dimer, other structures are found to coexist with the dominating T-shaped one for O(2)Ar and O(2)Xe.