The universal features of quantized thermal conductance of carbon nanotubes (CNTs) are revealed through a theoretical analysis based on the Landauer theory of heat transport. The phonon-derived thermal conductance of semiconducting CNTs exhibits a universal quantization in the low-temperature limit, independent of the radius or atomic geometry. The temperature dependence follows a single curve given in terms of temperature scaled by the phonon energy gap. The thermal conductance of metallic CNTs has an additional contribution from electronic states, which also exhibits quantized behavior up to room temperature.