Using fluorescence-based measurements, the effect of confinement on the glass transition temperature (T-g) was investigated in seven polymer systems of single-layer films supported on silicon substrates, all chosen such that they do not have substantial substrate interactions. Poly(vinyl chloride) exhibited the steepest reduction in T-g with decreasing film thickness. The largest magnitude of T-g reduction was observed in polysulfone where a 24-nm-thick film reported a T-g reduced by 53 degrees C relative to bulk. A system was also selected which exhibited no confinement effect at a thickness of 13-14 nm. Differential scanning calorimetry was used to determine dynamic fragilities in order to test the hypothesis that fragility is a key variable governing the magnitude of T-g-confinement effects. The systems in the present study show a one-to-one correlation between higher fragility and larger magnitudes of T-g reduction with decreasing film thickness. In particular, T-g/T-g,T-bulk exhibits a universal nature as a function of a scaled film thickness for all seven systems. Fragility is a key variable which reflects the local packing efficiency in a polymer glass and which determines the susceptibility of a glass former to perturbations, in this case induced by confinement.