We demonstrate theoretical and experimental techniques for manipulating the transverse spatial photonic degrees of freedom. Exploration of three interfero- metric systems, including a single beam-splitter and two distinct setups of the Mach-Zehnder type, reveals conditions necessary for observing Hong-Ou-Mandel interference between two photons, each in an arbitrary linear superposition of the two rst-order Hermite-Gaussian modes. For a Mach-Zehnder interferom- eter arranged to discriminate between modes of odd and even one-dimensional parity, we predict that if both input photons are in a balanced, in-phase su- perposition of the rst-order modes, the resulting interference will alter the transverse wavefunctions of the photons to be of Laguerre-Gaussian form. For a balanced Mach-Zehnder interferometer, we nd that HOMI can be observed for input photons in distinguishable transverse spatial modes. We experimen- tally test the one-dimensional parity-based Mach-Zehnder for inputs of classical coherent laser beams and nd that perfect constructive and destructive inter- ference, at either output port, occurs under HOMI conditions. In addition, we demonstrate the ability of this interferometer to sort inputs of arbitrary spatial modes into their odd and even constituent modes.