  We analyze archived Chandra and XMM-Newton X-ray observations of 536 Sloan
Digital Sky Survey (SDSS) Data Release 5 (DR5) quasars (QSOs) at 1.7 <= z <=
2.7 in order to characterize the relative UV and X-ray spectral properties of
QSOs that do not have broad UV absorption lines (BALs). We constrain the
fraction of X-ray weak, non-BAL QSOs and find that such objects are rare; for
example, sources underluminous by a factor of 10 comprise $\la$2% of
optically-selected SDSS QSOs. X-ray luminosities vary with respect to UV
emission by a factor of $\la$2 over several years for most sources. UV
continuum reddening and the presence of narrow-line absorbing systems are not
strongly associated with X-ray weakness in our sample. X-ray brightness is
significantly correlated with UV emission line properties, so that relatively
X-ray weak, non-BAL QSOs generally have weaker, blueshifted CIV$\lambda$1549
emission and broader CIII]$\lambda$1909 lines. The CIV emission line strength
depends on both UV and X-ray luminosity, suggesting that the physical mechanism
driving the global Baldwin effect is also associated with X-ray emission.
