We have studied the electrical and optical characteristics GaN/InGaN based light-emitting diodes (LEDs) grown on sapphire using metalorganic chemical vapor deposition (MOCVD). Strong correlation has been found between material quality and the mechanism of current transport through the wide-bandgap p-n junction. Tunneling behavior dominates throughout all injection regimes in the devices with high-density defects in the space-charge region, which act as deep-level carrier traps. The approximately current-squared dependence of light output at low currents indicates dominant nonradiative recombination in the active region. However, in a high quality LED diode, tunneling current is only a major contributor at low forward biases. At moderate biases, temperature dependent diffusion-recombination current has been identified as I0 exp(qV/1.6kT). In these devices, nonradiative recombination centers are saturated at current densities as low as 1.4×10-2 A/cm2.