Carbon K-edge X-ray spectroscopy has been applied to the study of a wide range of organic samples, from polymers and coals to interstellar dust particles. Identification of carbonaceous materials within these samples is accomplished by the pattern of resonances in the 280-320 eV energy region. Carbonate minerals are often encountered in the study of natural samples, and have been identified by a distinctive resonance at 290.3 eV. Here C K-edge and Ca L-edge spectra from a range of carbonate minerals are presented. Although all carbonates exhibit a sharp 290 eV resonance, both the precise position of this resonance and the positions of other resonances vary among minerals. The relative strengths of the different carbonate resonances also vary with crystal orientation to the linearly polarized X-ray beam. Intriguingly, several carbonate minerals also exhibit a strong 288.6 eV resonance, consistent with the position of a carbonyl resonance rather than carbonate. Calcite and aragonite, although indistinguishable spectrally at the C K-edge, exhibited significantly different spectra at the Ca L-edge. The distinctive spectral fingerprints of carbonates provide an identification tool, allowing for the examination of such processes as carbon sequestration in minerals, Mn substitution in marine calcium carbonates (dolomitization) and serpentinization of basalts.