We investigate theoretically the instantaneous hydrodynamic interaction between two identical, arbitrarily shaped particles suspended in a viscous fluid. We derive a general expression for the interaction at large inter-particle distances and apply it to two problems: (a) The orientational alignment of particles by external forcing; we show that the hydrodynamic interaction degrades the alignment, restricting its feasibility to low volume fractions. (b) The symmetry-based criteria for two particles to hydrodynamically attract or repel each other under identical forcing (hydrodynamic pseudo-potentials).