OSHA as an entity does not have any strict requirements regarding the spacing of cubicles. What it does concern itself with is office-space compliance with fire-code regulations expressed by the NFPA (National Fire Protection Association). This means that OSHA's oversight essentially covers means of evacuation or egress procedures should there be a fire-related emergency in a cubicle-defined environment.
Safety boards reference the Department of Labor as a model for cubicle guidelines. The state of North Carolina's Department of Health and Human Services uses the average Department of Labor entranceway to a cubicle—about 36 inches—as a guideline. All bookshelves and other pieces of modular furniture found within cubicles should be as needed only, and not excessive so as to limit the freedom of movement available to the employee. NFPA states that none of these pieces should "impact or interfere with egress" in the event of an evacuation of that office, floor or building.
While there is no formal law declaring that cubicles should be seen as legally-defined rooms per se, the general conclusion is that entrances into cubicles should accommodate people with handicaps or disabilities. This essentially falls under the purview of the Americans With Disabilities Act, especially with regard to offices that perform public functions. Therefore, you should ideally be able to introduce a wheel chair or any other items that aid the disabled into the doorway of a cubicle. Their introduction should not impede egress in any way.
Other guidelines taken from the North Carolina DHHS and their referencing of the Department of Labor establish further spatial norms. Walkways between cubicles are to be at least three feet and allow for easy flow of movement. The same width also describes a passageway of a side room into a main room or hallway leading to the exits. While these examples are specific to one state agency's interpretation, they should provide an adequate starting point for further investigation.