Timing observations from the Parkes 64-m radio telescope for 165 pulsars between 1990 and 2011 have been searched for period glitches. A total of 107 glitches were identified in 36 pulsars, where 61 have previously been reported and 46 are new discoveries. Glitch parameters were measured by fitting the timing residual data. Observed relative glitch sizes Delta u_g/ u range between 10^-10 and 10^-5, where u = 1/P is the pulse frequency. We confirm that the distribution of Delta u_g/ u is bimodal with peaks at approximately 10^-9 and 10^-6. Glitches are mostly observed in pulsars with characteristic ages between 10^3 and 10^5 years, with large glitches mostly occurring in the younger pulsars. Exponential post-glitch recoveries were observed for 27 large glitches in 18 pulsars. The fraction Q of the glitch that recovers exponentially also has a bimodal distribution. Large glitches generally have low Q, typically a few per cent, but large Q values are observed in both large and small glitches. Observed time constants for exponential recoveries ranged between 10 and 300 days with some tendency for longer timescales in older pulsars. Shorter timescale recoveries may exist but were not revealed by our data which typically have observation intervals of 2 - 4 weeks. For most of the 36 pulsars with observed glitches, there is a persistent linear increase in dot u in the inter-glitch interval. Where an exponential recovery is also observed, the effects of this are superimposed on the linear increase in dot u. In some cases, the slope of the linear recovery changes at the time of a glitch. The ddot u values characterising the linear changes in dot u are almost always positive and, after subtracting the magnetospheric component of the braking, are approximately proportional to the ratio of |dot u| and the inter-glitch interval, as predicted by vortex-creep models.
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