Rydberg spectra are shown to provide a spectral fingerprint that is sensitive to molecular structure in unique ways. The concepts are demonstrated using a set of isomeric fluorophenols and a sequence of aliphatic diamines. In the fluorophenols, the sensitivity extends to the placement of a single hydrogen atom and can be traced to the molecular charge distributions associated with the locations of atoms and functional groups with respect to the charge center. Experiments on tetramethyl diamines demonstrate that the structural sensitivity encompasses the extended molecular structure, including parts of the molecule that are remote from the ionization center. This global structure sensitivity makes Rydberg fingerprint spectroscopy uniquely suited to characterize structures of large-scale molecular systems.