This catalog contains some of the results of an investigation into the X-ray properties of radio-intermediate and radio-loud quasars (RIQs and RLQs, respectively). The authors have combined large, modern optical (e.g., SDSS) and radio (e.g., FIRST) surveys with archival X-ray data from Chandra, XMM-Newton, and ROSAT to generate an optically selected sample that includes 188 RIQs and 603 RLQs. This sample is constructed independently of X-ray properties but has a high X-ray detection rate (85%); it provides broad and dense coverage of the luminosity-redshift (l-z) plane, including at high redshifts (22% of the objects have z = 2-5), and it extends to high radio-loudness R_L values (33% of objects have R_L = log(L_r/L_o) = 3 - 5), where L_r and L_o are the rest-frame monochromatic luminosities at 5 GHz and 2500 Angstroms, respectively). The authors measure the "excess" X-ray luminosity of RIQs and RLQs relative to radio-quiet quasars (RQQs) as a function of radio loudness and luminosity, and parametrize the X-ray luminosity of RIQs and RLQs both as a function of optical/UV luminosity and also as a joint function of optical/UV and radio luminosity. RIQs are only modestly X-ray bright relative to RQQs; it is only at high values of radio loudness (R_L >~ 3.5) and radio luminosity that RLQs become strongly X-ray bright. This HEASARC table contains the primary sample from the reference paper. The authors consider three categories of quasars in this work: RQQs, RIQs, and RLQs (rather than just RQQs and RLQs), where the define RIQs to consist of objects with 1 <= R_L < 2; consequently, the objects they classify as RLQs satisfy R_L >= 2. The primary sample contained herein consists of 654 optically selected RIQs and RLQs with SDSS/FIRST observations and high-quality X-ray coverage from Chandra (171), XMM-Newton (202), or ROSAT (281). The primary sample is split nearly evenly between spectroscopic (312) and high-confidence photometric (342) quasars. Most (562) of the primary sample objects possess serendipitous off-axis X-ray coverage, while the remainder (92) were targeted in the observations used in this sample. The X-ray detection fraction for the primary sample is 84%; the detection fraction for those objects with Chandra/XMM-Newton/ROSAT coverage is 95%/92%/70% (typical ROSAT observations are comparatively less sensitive and have higher background). The authors adopt a standard cosmology with H₀ = 70 km s^-1 Mpc^-1, Omega_M = 0.3, and Omega_Lambda = 0.7 throughout their study. This table was created by the HEASARC in October 2012 based on <a href="https://cdsarc.cds.unistra.fr/ftp/cats/J/ApJ/726/20">CDS Catalog J/ApJ/726/20</a> file table1.dat. This is a service provided by NASA HEASARC .