A compilation of data for small molecule organic, polymeric, and inorganic glass-forming liquids shows that the original expectation, that there be a positive correlation between the thermodynamic measure of fragility C-p(l)/C-p(g) (or C-p(l)/C-p(c)) and the dynamic fragility index m, is not generally true. The results are consistent with three classes of behavior: (1) a decrease in m with increasing C-p(l)/C-p(g) for the polymeric glass formers; (2) a nearly constant value of m independent of C-p(l)/C-p(c) for small molecule organics and hydrogen bonding small molecules; (3) an increasing value of m with increasing C-p(l)/C-p(c) for inorganic glass formers as originally considered by Angell. (C) 2001 American Institute of Physics.