Organic scintillator materials have long been used as radiation detectors. They offer simultaneous detection of fast neutrons and gamma rays for applications in nuclear nonproliferation, international safeguards, and national security. The recent development of high quality stilbene crystals with excellent neutron-gamma pulse shape discrimination (PSD) has generated renewed interest in using crystalline materials. However, crystal organic scintillators are subject to a directional dependence in their response to heavy charged particle interactions, degrading their energy resolution for neutron measurements and worsening their PSD performance. This dissertation presents several studies that experimentally characterize the scintillation anisotropy in organic crystal scintillators. These include measurements of neutron, gamma-ray and cosmic muon interactions in anthracene, a historical benchmark among organic scintillator materials, to confirm and extend measurements previously available in the literature. The gamma-ray and muon measurements provide new experimental confirmation that no scintillation anisotropy is present in their interactions. Observations from these measurements have updated the hypothesis for the physical mechanism that is responsible for the scintillation anisotropy concluding that a relatively high dE/dx is required in order to produce a scintillation anisotropy. The directional dependence of the scintillation output in liquid and plastic materials was measured to experimentally confirm that no scintillation anisotropy correlated to detector orientation exists in amorphous materials. These observations confirm that the scintillation anisotropy is not due to an external effect on the measurement system, and that a fixed, repeating structure is required for a scintillation anisotropy. The directional dependence of the scintillation output in response to neutron interactions was measured in four stilbene crystals of various sizes and growth-methods. The scintillation anisotropy in these materials was approximately uniform, indicating that the crystal size, geometry, and growth method do not significantly impact the effect. Measurements of three additional pure crystals and two mixed crystals were made. These measurements showed that 1) the magnitude of the effect varies with energy and material, 2) the relationship between the light output and pulse shape anisotropy varies across materials, and 3) the effect in mixed materials is very complex. These measurements have informed the hypothesis of the mechanism that produces the directional dependence. By comparing the various relationships between the light output and pulse shape anisotropy across materials, these measurements indicate that the preferred directions of singlet and triplet excitation transport may be the same in some materials and different in other materials. The measurements performed in this work serve as a resource to groups who aim to correct for the scintillation anisotropy or employ it as a directional detection modality. Additionally, this work has advanced the understanding of what physical processes and properties dictate the magnitude and behavior of the scintillation anisotropy in a given material. It has added new information to the body of knowledge surrounding the scintillation mechanism in organic crystal scintillator materials. This information may be used to construct models to predict the scintillation anisotropy effect in materials that have not been experimentally characterized. Such work can contribute to work in producing a new generation of organic scintillator materials, advancing many applications in nuclear science and security.