To investigate the merits of crystal structure prediction using ab initio computational techniques, we have used density functional (DFT) methods to investigate the relative stabilities of the four known crystalline phases of glycine and also a range of alternative putative crystal structures of the zwitterion. Energy differences are calculated using a range of exchange-correlation functionals, and it is found that the calculated relative stability of the phases is sensitive to the choice of functional. Energy differences are found to be on the order of a few tenths of a kilocalorie per mole with little separation in energy found between observed and putative structures. This result is similar to that typically obtained from force field calculations and confirms the difficulty of the task of predicting the structure of molecular crystals. Optimization of structures, including optimization of unit cells, highlights the limitation of DFT in describing the long-range dispersion interaction. Use of the local density approximation (LDA) is shown to over-bind crystals, whereas use of gradient-corrected functionals severely under-binds crystals. Calculated structural energy differences are presented, which show that, for the case of the LDA, the four observed glycine polymorphs receive a lower energy than all putative glycine structures considered.