We present the results of a survey for intervening H i 21-cm absorbers at intermediate and low redshift (0 < z < 1.2). For our total sample of 24 systems, we obtained high-quality data for 17 systems, the other seven being severely affected by radio frequency interference (RFI). Five of our targets are low-redshift (z < 0.17) optical galaxies with small impact parameters (<20 kpc) towards radio-bright background sources. Two of these were detected in 21-cm absorption, showing narrow, high optical depth absorption profiles, the narrowest having a velocity dispersion of only 1.5 km s− 1, which puts an upper limit on the kinetic temperature of Tk < 270 K. Combining our observations with results from the literature, we measure a weak anticorrelation between impact parameter and integral optical depth in local (z < 0.5) 21-cm absorbers. Of 11 Ca ii and Mg ii systems searched, two were detected in 21-cm absorption, and six were affected by RFI to a level that precludes a detection. For these two systems at z ∼ 0.6, we measure spin temperatures of Ts = (65 ± 17) K and Ts > 180 K. A subset of our systems was also searched for OH absorption, but no detections were made.