Quasi-stellar objects (QSOs) whose spectral energy distributions (SEDs) are reddened by dust either in their host galaxies or in intervening absorber galaxies are to a large degree missed by optical color selection criteria like the ones used by the Sloan Digital Sky Survey (SDSS). To overcome this bias against red QSOs, we employ a combined optical and near-infrared (near-IR) color selection. In this paper, we present a spectroscopic follow-up campaign of a sample of red candidate QSOs which were selected from the SDSS and the UKIRT Infrared Deep Sky Survey (UKIDSS). The spectroscopic data and SDSS/UKIDSS photometry are supplemented by mid-infrared photometry from the Wide-field Infrared Survey Explorer. In our sample of 159 candidates, 154 (97%) are confirmed to be QSOs. We use a statistical algorithm to identify sightlines with plausible intervening absorption systems and identify nine such cases assuming dust in the absorber similar to Large Magellanic Cloud sightlines. We find absorption systems toward 30 QSOs, 2 of which are consistent with the best-fit absorber redshift from the statistical modeling. Furthermore, we observe a broad range in SED properties of the QSOs as probed by the rest-frame 2 mu m flux. We find QSOs with a strong excess as well as QSOs with a large deficit at rest-frame 2 mu m relative to a QSO template. Potential solutions to these discrepancies are discussed. Overall, our study demonstrates the high efficiency of the optical/near-IR selection of red QSOs.