The key role of chain flexibility in polymer glass formation has long been appreciated, but a fundamental understanding of how chain stiffness influences polymer glass formation remains elusive. In this work, we systematically investigate glass formation in unentangled linear polymer melts having variable chain stiffness using molecular dynamics simulation. Basic thermodynamic and dynamic properties are systematically analyzed upon approaching the glass transition, leading to general accord with the predictions from the generalized entropy theory (GET). As a general finding, chain stiffness is found to have rather limited influence on the temperature dependence of the basic thermodynamic properties considered. As expected, the characteristic temperatures and fragility of glass formation grow with increasing chain stiffness, but these quantities are found to plateau when the chains become sufficiently stiff, exactly the same trends predicted by the GET. We further find a universal reduction of the structural relaxation time in polymer melts having variable chain stiffness based on the string model of glass formation, which, in turn, allows us to estimate the enthalpy and entropy of the high temperature activation free energy, parameters that play a fundamental role in describing and understanding the dynamics of liquids within the framework of transition state theory. This analysis emphasizes the necessity of keeping the entropic term of the activation free energy in predicting the structural relaxation time of glass forming liquids, providing a crucial hint for how the GET might be improved to quantitatively predict the dynamics of glass forming polymers. The relationship between the structural relaxation time and certain measures of dynamic heterogeneity is also discussed in our model polymer melts with varying chain stiffness. Our results provide a starting point for studying the glass formation in more complicated polymeric systems, e.g., polymers with explicit monomer structures and ionic liquids, systems that are of both fundamental interest and practical significance.