Using Green Bank Telescope radio recombination line (RRL) data, we analyze the role of leaking radiation from H II regions in maintaining the ionization of the interstellar medium. We observed a sample of eight Galactic H II regions of various sizes, morphologies, and luminosities. For each region the hydrogen RRL intensity decreases roughly as a power-law with distance from the center of the region. This suggests that radiation leaking from the H II region is responsible for the majority of surrounding ionized gas producing RRL emission. Our results further indicate that the hydrogen RRL intensity appears to be fundamentally related to the H II region sizes traced by their photodissociation regions, such that physically smaller H II regions show a steeper decrease in intensity with increasing distance from the region centers. As a result, giant H II regions may have a much larger effect in maintaining the ionization of the interstellar medium. For six of the eight observed H II regions we find a decrease in the 4 He + /H + abundance ratio with increasing distance, indicating that He-ionizing photons are being absorbed within the ionization front of the H II region. There is enhanced carbon RRL emission toward directions with strong continuum background, suggesting that the carbon emission is amplified by stimulated emission.