The ROSAT All-Sky Survey (RASS) was the first imaging X-ray survey of the entire sky. While X-ray source counterparts are known to range from distant quasars to nearby M dwarfs, the RASS data alone are often insufficient to determine the nature of an X-ray source. As a result, large-scale follow-up programs are required to construct samples of known X-ray emitters. We use optical data produced by the Sloan Digital Sky Survey (SDSS) to identify 709 stellar X-ray emitters cataloged in the RASS and falling within the SDSS Data Release 1 footprint. Most of these are bright stars with coronal X-ray emission unsuitable for SDSS spectroscopy, which is designed for fainter objects (g > 15 mag). Instead, we use SDSS photometry, correlations with the Two Micron All Sky Survey and other catalogs, and spectroscopy from the Apache Point Observatory 3.5 m telescope to identify these stellar X-ray counterparts. Our sample of 707 X-ray-emitting F, G, K, and M stars is one of the largest X-ray-selected samples of such stars. We derive distances to these stars using photometric parallax relations appropriate for dwarfs on the main sequence, and use these distances to calculate LX. We also identify a previously unknown cataclysmic variable (CV) as a RASS counterpart. Separately, we use correlations of the RASS and the SDSS spectroscopic catalogs of CVs and white dwarfs (WDs) to study the properties of these rarer X-ray-emitting stars. We examine the relationship between (fX/fg) and the equivalent width of the Hbeta emission line for 46 X-ray-emitting CVs and discuss tentative classifications for a subset based on these quantities. We identify 17 new X-ray-emitting DA (hydrogen) WDs, of which three are newly identified WDs. (abridged)
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