We discuss the thermal pressures (n H T) in predominantly cold, neutral interstellar gas in the Magellanic Clouds, derived from analyses of the fine-structure excitation of neutral carbon, as seen in high-resolution Hubble Space Telescope/Space Telescope Imaging Spectrograph spectra of seven diverse sight lines in the LMC and SMC. Detailed fits to the line profiles of the absorption from C I, C I * , and C I ** yield consistent column densities for the three to six C I multiplets detected in each sight line. In the LMC and SMC, N(C I tot ) is consistent with Galactic trends versus N(Na I) and N(CH), but is slightly lower versus N(K I) and N(H 2 ). As for N(Na I) and N(K I), N(C I tot ) is generally significantly lower, for a given N(H tot ), in the LMC and (especially) in the SMC, compared to the local Galactic relationship. For the LMC and SMC components with well-determined column densities for C I, C I * , and C I ** , the derived thermal pressures are typically factors of a few higher than the values found for most cold, neutral clouds in the Galactic ISM. Such differences are consistent with the predictions of models for clouds in systems (like the LMC and SMC) that are characterized by lower metallicities, lower dust-to-gas ratios, and enhanced radiation fields-where higher pressures are required for stable cold, neutral clouds. The pressures may be further enhanced by energetic activity (e.g., due to stellar winds, star formation, and/or supernova remnants) in several of the regions probed by these sight lines. Comparisons are made with the C I observed in some quasar absorption-line systems.