We present an analysis of bulk H-1 NMR chemical shifts for a series of biochemically relevant molecular crystals in analogy to the well-known solvent NMR chemical shifts. The term bulk shifts denotes the change in NMR frequency of a gas-phase molecule when it undergoes crystallization. We compute NMR parameters from first-principles electronic structure calculations under full periodic boundary conditions and for isolated molecules and compare them to the corresponding experimental fast magic-angle spinning solid-state NMR spectra. The agreement between computed and experimenal lines is generally very good. The main phenomena responsible for bulk shifts are packing effects (hydrogen bonding and pi-stacking) in the condensed phase. By using these NMR bulk shifts in well-ordered crystalline model systems composed of biologically relevant molecules, we can understand the individual spectroscopic signatures of packing effects. These local structural driving forces, hydrogen bonding, pi-stacking, and related phenomena, stand as a model for the forces that govern the assembly of much more complex supramolecular aggregates. We show to which accuracy condensed-phase ab initio calculations can predict structure and structure-property relationships for noncovalent interactions in complex supramolecular systems.