The monolayer phase diagrams for a number of nonpolar, linear molecules adsorbed on the basal plane of graphite are reviewed. Values for some of the transition temperatures such as the 2D gas-liquid critical points and the melting points of the low-density 2D solids are collected. Upon comparison of these data with each other and with the analogous data for some spherical adsorbate molecules on graphite, it is argued that the ratios of the 2D critical temperatures to the bulk 3D critical temperatures for these linear molecules are essentially independent of molecular shape and quadrupole moment. The melting points are much more sensitive to the details of the molecular size and shape, but two major categories can be discerned : weakly quadrupolar molecules which form 2D lattices with all molecules lying parallel to one another and are often incommensurate, and strongly quadrupolar molecules that form herringbone lattices which are often commensurate with the underlying substrate lattice. When molecular orientation changes greatly upon melting, it is found that melting points are abnormally low compared to the systems where this does not occur.