A significant fraction (~30%) of the high-energy {gamma}-ray sources listed in the second Fermi Large Area Telescope (LAT) catalog are still of unknown origin, having not yet been associated with counterparts at lower energies. To investigate the nature of these enigmatic sources, we present an extensive search of X-ray sources lying in the positional uncertainty region of a selected sample of these unidentified gamma-ray sources (UGSs) that makes use of all available observations performed by the Swift X-ray Telescope before 2013 March 31, available for 205 UGSs. To detect the fainter sources, we merged all the observations covering the Fermi LAT positional uncertainty region at a 95% level of confidence of each UGS. This yields a catalog of 357 X-ray sources, finding candidate X-ray counterparts for ~70% of the selected sample. In particular, 25% of the UGSs feature a single X-ray source within their positional uncertainty region, while 45% have multiple X-ray sources. For each X-ray source, we also looked in the corresponding Swift UVOT merged images for optical and ultraviolet counterparts, also performing source photometry. We found ultraviolet-optical correspondences for ~70% of the X-ray sources. We searched several major radio, infrared, optical, and ultraviolet surveys for possible counterparts within the positional error of the sources in the X-ray catalog to obtain additional information on their nature. Applying the kernel density estimation technique to infrared colors of Wide-Field Infrared Survey Explorer counterparts of our X-ray sources we select six {gamma}-ray blazar candidates. In addition, comparing our results with previous analyses, we select 11 additional {gamma}-ray blazar candidates.