Pair and bond-orientational correlation functions and structure factors, as used in colloidal science, are applied as quantitative indicators of the phase of the newly discovered ''plasma crystals.'' These Coulomb-lattice structures are formed by charged microspheres levitated in glow discharge plasmas and are imaged photographically. Static structural analysis is demonstrated on the experimental data of Thomas et al. [Phys. Rev. Lett. 73, 652, (1994)] and interpreted in the context of a two-dimensional (2D) dislocation-unbinding melting theory and a 2D density-wave melting theory.