We present low-resolution optical spectra for 29 X-ray sources identified as either massive star candidates or low-mass pre-main-sequence (PMS) star candidates in the clusters Trumpler 16 and Trumpler 14 of the Carina Nebula. Spectra of two more objects (one with an X-ray counterpart, and one with no X-ray counterpart), not originally our targets, but found close (∼3″) to two of our targets, are presented as well. Twenty early-type stars, including an O8 star, seven B1-B2 stars, two B3 stars, a B5 star, and nine emission-line stars, are identified. Eleven T Tauri stars, including eight classical T Tauri stars (CTTSs) and three weak-lined T Tauri stars, are identified. The early-type stars in our sample are more reddened compared to the previously known OB stars of the region. The Chandra hardness ratios of our T Tauri stars are found to be consistent with the Chandra hardness ratios of T Tauri stars of the Orion Nebula Cluster. Most early-type stars are found to be nonvariable in X-ray emission, except the B2 star J104518.81-594217.9, the B3 star J104507.84-594134.0, and the Ae star J104424.76-594555.0, which are possible X-ray variables. J104452.20-594155.1, a CTTS, is among the brightest and the hardest X-ray sources in our sample, appears to be a variable, and shows a strong X-ray flare. The mean optical and near-infrared photometric variability in the V and Ks bands, of all sources, is found to be ∼0.04 and 0.05 mag, respectively. The T Tauri stars show significantly larger mean variation, ∼0.1 mag, in the Ks band. The addition of one O star and seven B1-B2 stars reported here contributes to an 11% increase of the known OB population in the observed field. The 11 T Tauri stars are the first ever confirmed low-mass PMS stars in the Carina Nebula region.