The Galactic Arecibo L-band Feed Array H I (GALFA-H I) survey is mapping the entire Arecibo sky at 21 cm, over a velocity range of -700 to +700 km/s (LSR), at a velocity resolution of 0.18 km/s, and a spatial resolution of 3.5 arcmin. The unprecedented resolution and sensitivity of the GALFA-H I survey have resulted in the detection of numerous isolated, very compact H I clouds at low Galactic velocities, which are distinctly separated from the H I disk emission. In the limited area of ~4600 deg^2^ surveyed so far, we have detected 96 such compact clouds. The detected clouds are cold with a median T_k,max_ (the kinetic temperature in the case in which there is no non-thermal broadening) of 300 K. Moreover, these clouds are quite compact and faint, with median values of 5 arcmin in angular size, 0.75 K in peak brightness temperature, and 5x10^18^/cm2 in H I column density. Most of the clouds deviate from Galactic rotation at the 20-30 km/s level, and a significant fraction show evidence for a multiphase medium and velocity gradients. No counterparts for these clouds were found in other wave bands. From the modeling of spatial and velocity distributions of the whole compact cloud population, we find that the bulk of the compact clouds are related to the Galactic disk, and their distances are likely to be in the range of 0.1 to a few kpc. We discuss various possible scenarios for the formation and maintenance of this cloud population and its significance for Galactic interstellar medium studies.