We have conducted a new Arecibo survey for H I emission for 113 galaxies with broad-line (type 1) active galactic nuclei (AGNs) out to recession velocities as high as 35,000 km/s. The primary aim of the study is to obtain sensitive H I spectra for a well-defined, uniformly selected sample of active galaxies that have estimates of their black hole masses in order to investigate correlations between H I properties and the characteristics of the AGNs. H I emission was detected in 66 out of the 101 (65%) objects with spectra uncorrupted by radio frequency interference, among which 45 (68%) have line profiles with adequate signal-to-noise ratio and sufficiently reliable inclination corrections to yield robust deprojected rotational velocities. This paper presents the basic survey products, including an atlas of H I spectra, measurements of H I flux, line width, profile asymmetry, optical images, optical spectroscopic parameters, as well as a summary of a number of derived properties pertaining to the host galaxies. To enlarge our primary sample, we also assemble all previously published H I measurements of type 1 AGNs for which can can estimate black hole masses, which total an additional 53 objects. The final comprehensive compilation of 154 broad-line active galaxies, by far the largest sample ever studied, forms the basis of our companion paper, which uses the H I database to explore a number of properties of the AGN host galaxies.