The identification of six X-ray sources discovered by the Einstein Observatory with X-ray quasars is reported, and the properties of these X-ray selected quasars are discussed. The four high-latitude fields of 1 sq deg each in which the Einstein imaging proportional counter detected serendipitous X-ray sources at intermediate exposures of 10,000 sec were observed by 4-m and 1.5-m telescopes, and optical sources with uv excesses and emission line spectra typical of many low-redshift quasars and Seyfert 1 galaxies were found within the 1-arcsec error boxes of the X-ray sources. All six quasars identified were found to be radio quiet, with low redshift and relatively faint optical magnitudes, and to be similar in space density, colors and magnitude versus redshift relation to an optically selected sample at the same mean magnitude. X-ray luminosity was found to be well correlated with both continuum and broad-line emission luminosities for the known radio-quiet quasars and Seyfert 1 galaxies, and it was observed that the five objects with the lowest redshifts have very similar X-ray/optical luminosity ratios despite tenfold variations in X-ray luminosity. It is concluded that photoionization by a continuum extending to X-ray energies is the dominant excitation mechanism in radio-quiet quasars.