Timing observations of 40 mostly young pulsars using the ATNF Parkes radio telescope between 1990 January and 1998 December are reported. In total, 20 previously unreported glitches and ten other glitches were detected in 11 pulsars. These included 12 glitches in PSR J1341$- $6220, corresponding to a glitch rate of 1.5 glitches per year. We also detected the largest known glitch, in PSR J1614$-$5047, with $\Delta\nu_g/\nu \approx 6.5 \times 10^{-6}$ where $\nu = 1/P$ is the pulse frequency. Glitch parameters were determined both by extrapolating timing solutions to inter-glitch intervals and by phase-coherent timing fits across the glitch(es). Analysis of glitch parameters, both from this work and from previously published results, shows that most glitches have a fractional amplitude $\Delta\nu_g/\nu$ of between $10^{-8}$ and $10^{-6}$. There is no consistent relationship between glitch amplitude and the time since the previous glitch or the time to the following glitch, either for the ensemble or for individual pulsars. As previously recognised, the largest glitch activity is seen in pulsars with ages of order 10$^4$ years, but for about 30 per cent of such pulsars, no glitches were detected in the 8-year data span. There is some evidence for a new type of timing irregularity in which there is a significant increase in pulse frequency over a few days, accompanied by a decrease in the magnitude of the slowdown rate. Fits of an exponential recovery to post-glitch data show that for most older pulsars, only a small fraction of the glitch decays. In some younger pulsars, a large fraction of the glitch decays, but in others, there is very little decay.