The fragility parameter has been acknowledged as one of the most important characteristics of glass-forming liquids. We show that the mystery of the dramatic change in molecular dynamics of systems approaching the glass transition can be better understood by the high pressure study of fragility parameters defined in different thermodynamic conditions. We formulate and experimentally confirm a few rules obeyed by the fragility parameters, which are also rationalized by the density scaling law and its modification suggested for associated liquids. In this way, we successfully explore and gain a new insight into the pressure effect on molecular dynamics of van der Waals liquids, polymer melts, ionic liquids, and hydrogen-bonded systems near the glass transition.