Measurements of [CI], J = 2-1 13CO and J = 4-3 12 CO emission from quiescent, starburst and active galaxy centers reveal a distinct pattern characterized by relatively strong [CI] emission. The [CI] to 13co emission ratio increases with central [CI] luminosity. It is lowest in quiescent and mild starburst centers and highest for strong starburst centers and active nuclei. C° abundances are close to, or even exceed, CO abundances. The emission is characteristic of warm and dense gas rather than either hot tenuous or cold very dense gas. The relative intensities of CO, [CI], [CII] and far-infrared emission suggest that the dominant excitation mechanism in galaxy centers may be different from that in photon-dominated regions (PDRs).