The fundamental reasons that determine the tolerance of free-space optical interconnect systems to misalignment are considered. By evaluation of the overlap of single-mode optical beams in the presence of misalignment it possible to determine an optimum beam configuration. It is shown that for any level of misalignment there is an optimum beam diameter that maximizes the coupling of light through the system. Many interconnect systems are not single mode throughout, so the analysis is extended to cover multimode systems. It is shown that, in principle, any level of misalignment can be accommodated by use of multimode beams, although at the cost of reduced channel density. It is shown that the presence of misalignment will mean that the number of channels that can be supported by an interconnect reduces with the length of the interconnect. As possible candidates for passively aligned systems, three example optical systems are analyzed by use of the methods developed.