Solution theories currently in use by chemical engineers (regular solutions, conformal solution theory, etc.) are based on an oversimplified view of the intermolecular forces, so that they are strictly valid only for such simple fluids as argon. We present here a solution theory (based on thermodynamic perturbation theory) which allows strong directional inter-molecular forces to be taken into account when calculating thermodynamic properties. This theory is in excellent agreement with computer simulation results for strongly polar or quadrupolar fluids. It is applied to the prediction of phase equilibrium surfaces, critical loci, three-phase lines, and azeotropic loci for mixtures containing constituents with (a) polar, (b) quadrupolar, and (c) anisotropic shape (charge overlap) intermolecular forces. The relation between these intermolecular forces and the type of phase behaviour is explored for binary mixtures. The anisotropic shape forces have little effect on the phase diagram; however, a wide variety of phase behaviour is found for the other cases. Mixtures with polar or quadrupolar constituents are shown to give rise to five of the six classes of binary phase diagrams found in nature.