We measure Galactic interstellar neutral hydrogen column densities by analyzing archival interstellar Ly{alpha} absorption line data toward 554 B2 and hotter stars observed at high resolution with the IUE satellite. This study more than doubles the number of lines of sight with measures of N(H I) based on Ly{alpha}. We have included the scattered light background correction algorithm of Bianchi and Bohlin (1984A&A...134...31B) in our data reduction. We use the correlation between the Balmer discontinuity [c_1_] index and the stellar Ly{alpha} absorption in order to assess the effects of stellar Ly alpha contamination. Approximately 40% of the B stars with measured [c_1_] index, exhibit serious stellar Ly{alpha} contamination. Table 1 contains the derived values of the interstellar N(H I) for 393 stars with at most small amounts of stellar contamination. Table 2 lists the observed values of total N(H I) for 161 stars with suspected stellar Ly alpha contamination and/or uncertain stellar parameters.