Molecular devices have the potential to revolutionise many technologies, from computer architecture to chemical sensors and medical diagnostics. Such devices have been experimentally constructed using different techniques, and modelled with several computational methods. The method most commonly used to perform such calculations combines the non-equilibrium Green's function formalism (NEGF) with density functional theory (DFT). However, DFT calculations based on local exchange and correlation functionals contain self-interaction errors. The primary purpose of this work is to investigate the effects of these errors on electronic transport calculations. The origin of the self-interaction error in DFT will be described, as well as its consequences including the absence of the derivative discontinuity in approximate local exchange-correlation potentials. Exact and approximate self-interaction corrections to remove these errors will also be described. To demonstrate the effect of the self-interaction errors on electronic transport, we present results of calculations performed using the NEGF code SMEAGOL for a variety of metal-molecule junctions, particularly for benzenedithiol attached to gold. We use a tight-binding Hamiltonian to demonstrate that the presence of a derivative discontinuity in the energy can open conductance gaps in the I-V curves, which are predicted to be gapless otherwise. Then, an atomic self-interaction correction (ASIC) to DFT is used to investigate the effect of correcting the alignment between the energy levels in the molecule and the Fermi level in the metal. Both of these methods suppress the low-bias conductivity of metal-molecule junctions, improving the agreement between theory and experiment.