As part of a detailed study of the gas content in a sample of early-type galaxies, we present 21 cm H I line maps of the S0 galaxy NGC 404 at a spatial resolution of 15.2"'×14.4" (α×δ) and a velocity resolution of 2.6 km s-1. The H I has been traced out to a radius R~8R25 or 48 disk scale lengths, making it one of the largest H I extents reported (800" or 12.6 kpc at the assumed distance of 3.3 Mpc). Approximately 75% of the H I resides in a doughnut, which is seen close to face-on with inner and outer radii of ~R25 and ~4R25, respectively. The optical galaxy fits snugly within the hole of the doughnut. The remaining 25% of the neutral gas is found in an annulus concentric with the doughnut and with a somewhat larger ellipticity, extending from a radius of ~4R25 to ~8R25. A total H I mass of 1.52+/-0.04×108Msolar is found, which implies an MHI/LB=0.22 in solar units. We argue that most, if not all, of this gas is of external origin, most likely from the merger of a dwarf irregular galaxy with MB~-15.5 mag. The velocity field shows a steeply declining observed rotation curve, compatible with Keplerian decline. However, because the galaxy is close to face-on, there is a degeneracy in the determination of the intrinsic rotation curve and inclination. We therefore analyzed two extreme cases, producing tilted-ring model fits forcing either a Keplerian or a flat rotation curve through the observations; both approaches result in equally plausible fits. In both model fits, the position angle of the kinematical major axis of the annulus is distinct from that of the doughnut and ranges from 160° to 120° (for the doughnut these values are 100° to 60°). Assuming a distance of 3.3 Mpc, a total mass of 3×1010Msolar is found on the basis of the Keplerian rotation curve. This implies a global MT/LB ratio of ~44 in solar units, which is high and likely a reflection of the low blue luminosity of the galaxy (~15 times lower than the average S0 luminosity). Values for a flat rotation curve are a factor of 4 higher.