The spatial distribution of the H I gas in galactic disks holds important clues about the physical processes that shape the structure and dynamics of the interstellar medium (ISM). The structure of the ISM could be affected by a variety of perturbations internal and external to the galaxy, and the unique signature of each of these perturbations could be visible in the structure of interstellar gas. In this work, we quantify the structure of the H I gas in a sample of 33 nearby galaxies taken from the HI Nearby Galaxy Survey (THINGS) using the delta-variance (Delta-variance) spectrum. The THINGS galaxies display a large diversity in their spectra, but there are a number of recurrent features. In many galaxies, we observe a bump in the spectrum on scales of a few to several hundred parsec. We find the characteristic scales associated with the bump to be correlated with the galactic star formation rate (SFR) for values of the SFR greater than or similar to 0.5 M-circle dot yr(-1) and also with the median size of the H I shells detected in these galaxies. We interpret this characteristic scale as being associated with the effects of feedback from supernova explosions. On larger scales, we observe in most galaxies two self-similar, scale-free regimes. The first regime, on intermediate scales (less than or similar to 0.5R(25)), is shallow, and the power law that describes this regime has an exponent in the range [0.1-1] with a mean value of 0.55 that is compatible with the density field that is generated by supersonic turbulence in the cold phase of the H I gas. The second power law is steeper, with a range of exponents between 0.5 and 2.3 and a mean value of approximate to 1.5. These values are associated with subsonic to transonic turbulence, which is characteristic of the warm phase of the H I gas. The spatial scale at which the transition between the two self-similar regimes occurs is found to be approximate to 0.5R(25), which is very similar to the size of the molecular disk in the THINGS galaxies. Overall, our results suggest that on scales less than or similar to 0.5R(25), the structure of the ISM is affected by the effects of supernova explosions. On larger scales (greater than or similar to 0.5R(25)), stellar feedback has no significant impact, and the structure of the ISM is determined by large-scale processes that govern the dynamics of the gas in the warm neutral medium, such as the flaring of the H I disk at large galactocentric radii and the effects of ram pressure stripping.