Hard X-ray surveys performed by the INTEGRAL satellite have discovered a conspicuous fraction (up to 30%) of unidentified objects among the detected sources. Here we continue our program of identification of these objects by (i) selecting probable optical candidates by means of positional cross-correlation of the INTEGRAL detections with soft X-ray, radio, and/or optical archives and (ii) performing optical spectroscopy on them. As a result, we pinpointed and identified, or more accurately characterized, 44 definite or likely counterparts of INTEGRAL sources. Among them, 32 are active galactic nuclei (AGNs; 18 with broad emission lines, 13 with narrow emission lines only, and one X-ray bright, optically normal galaxy) with redshift 0.019 < z < 0.6058, 6 cataclysmic variables (CVs), 5 high-mass X-ray binaries (2 of which in the Small Magellanic Cloud), and 1 low-mass X-ray binary. This was achieved by using 7 telescopes of various sizes and archival data from two online spectroscopic surveys. The main physical parameters of these hard X-ray sources were also determined using the multiwavelength information available in the literature. In general, AGNs are the most abundant population among hard X-ray objects, and our results confirm the tendency of finding AGNs more frequently than any other type of hard X-ray emitting object among unidentified INTEGRAL sources when optical spectroscopy is used as an identification tool. Moreover, the deeper sensitivity of the more recent INTEGRAL surveys enables one to begin detecting hard X-ray emission above 20 keV from sources such as LINER-type AGNs and non-magnetic CVs.