We identify 814 discrete H I clouds in 40 dwarf irregular galaxies from the LITTLE THINGS survey using an automated cloud-finding algorithm. The cloud masses range from ~10^3^ to 10^7^ M_{sun}_, have a surface density averaged over all of the clouds of ~9.65 M_{sun}_/pc^2^, and constitute 2%-53% of the total H I mass of the host galaxy. For individual clouds, the mass including He varies with cloud radius as logM_gas_=(2.11+/-0.04)xlogR_cl_+(0.78+/-0.08) and the internal velocity dispersion varies as logV_disp_=0.5xlogR_cl_-0.57+/-0.21. The H I clouds tend to be in the outer regions of the galaxies, with 72% of the galaxies having more than 70% of their clouds outside one disk scale length and 32% of the galaxies having more than 50% of their clouds outside the radius encircling the H II emission. Thirty-six percent of the clouds are essentially non-self-gravitating from H I alone, with a virial parameter that exceeds {alpha}_vir_~10, and 5% have {alpha}_vir_=<2. We estimate the missing molecular mass, based on the total star formation rate and a typical molecular consumption time of 2 Gyr, as observed in CO-rich galaxies. The resulting molecular fraction has a value averaged over the galaxies of 0.23 and correlates with both the surface density of star formation and the fraction of H I clouds in the outer regions. We conclude that a significant fraction of the inner parts of these dwarf galaxy disks is in the form of dark molecular gas, and that this fraction could be high enough to make the inner disks mildly gravitationally unstable as a precursor to star formation.