We compile, from the existing literature, the largest sample to date (842 data points) of hydrogen column density measurements, N(HI), of the gas in the interstellar medium. We include only results obtained from absorption measurements toward individual stars (594 in our sample) in an effort to construct a three-dimensional picture of the interstellar gas. We derive hydrogen column densities toward a fraction of the stars in the sample from published column density measurements of metal ions. A three-dimensional physical model derived from this data set will be presented in a companion paper. The observed stars span distances from a few parsecs to a few thousand parsecs, and more than half of the sample serves to describe the local interstellar medium within a few hundred parsecs of the Sun. Hydrogen column densities range from 10^17^ to 10^22^cm^-2^. We describe here the various observational methods used to estimate the hydrogen column densities and present the table with the stellar and hydrogen column density data. The provided table is intended as a global reference work, not to introduce new results.