Sensitive H I 21cm emission line spectra have been measured for the directions to 143 quasars and AGNs chosen from the observing lists for the HST Quasar Absorption Line Key Project. Narrow-band and wide-band data were obtained with the NRAO 43m radio telescope for each object. The narrow-band data have a velocity resolution of 1km/s, extend from -220 to +170km/s, and are corrected for stray 21cm radiation. The wide-band data have a resolution of 4km/s and extend from -1000 to +1000km/s. The data are important for the interpretation of ultraviolet absorption lines near zero redshift in Key Project spectra. Twenty-two percent of the quasars lie behind Galactic high-velocity H I clouds with |VLSR|>100km/s whose presence can increase the equivalent width of interstellar absorption lines significantly. This paper contains the emission spectra and measures of the H I velocities and column densities along the sight line to each quasar. We discuss how the measurements can be used to estimate the visual and ultraviolet extinction toward each quasar and to predict the approximate strength of the strong ultraviolet resonance lines of neutral gas species in the HST Key Project spectra.