(Abridged) We report on the X-ray and multiwavelength properties of 11 radio-quiet quasars with weak or no emission lines identified by the Sloan Digital Sky Survey (SDSS) with redshift z=0.4-2.5. The distribution of relative X-ray brightness for our low-redshift weak-line quasar (WLQ) candidates is significantly different from that of typical radio-quiet quasars, having an excess of X-ray weak sources, but it is consistent with that of high-redshift WLQs. The X-ray weak sources generally show similar UV emission-line properties to those of the X-ray weak quasar PHL 1811; they may belong to the notable class of PHL 1811 analogs. The average X-ray spectrum of these sources is somewhat harder than that of typical radio-quiet quasars. Several other low-redshift WLQ candidates have normal ratios of X-ray-to-optical/UV flux, and their average X-ray spectral properties are also similar to those of typical radio-quiet quasars. The X-ray weak and X-ray normal WLQ candidates may belong to the same subset of quasars having high-ionization shielding gas covering most of the wind-dominated broad emission-line region, but be viewed at different inclinations. The mid-infrared-to-X-ray spectral energy distributions (SEDs) of these sources are generally consistent with those of typical SDSS quasars, showing that they are not likely to be BL Lac objects with relativistically boosted continua and diluted emission lines. However, one source in our X-ray observed sample is remarkably strong in X-rays, indicating that a small fraction of low-redshift WLQ candidates may actually be BL Lacs residing in the radio-faint tail of the BL Lac population. We also investigate universal selection criteria for WLQs over a wide range of redshift, finding that it is not possible to select WLQ candidates in a fully consistent way using different prominent emission lines as a function of redshift.
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