We present the results of a survey for intervening HI 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) toward 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, which puts an upper limit on the kinetic temperature of T_k<270 K. Combining our observations with results from the literature, we measure a weak anti-correlation between impact parameter and integral optical depth in local (z<0.5) 21-cm absorbers. Of eleven CaII and MgII 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 T_s=(65+/-17) K and T_s>180 K. A subset of our systems were also searched for OH absorption, but no detections were made.