Pulse arrival-time data spanning up to 7 yr are analysed in order to provide a description of the timing noise of 45 southern pulsars. The results show that (i) for 19 pulsars, the timing activity is very weak (rms noise typically less than or equal to 2 milliperiods), (ii) for seven pulsars, the timing activity can be attributed to a random walk process comprising a large number of unresolvable events in one of the rotation variables, (iii) for seven pulsars, the timing activity can be attributed to resolved jumps in the rotation frequency and frequency derivative, superimposed on a random walk process, (iv) for seven pulsars, the timing activity can be attributed to resolved jumps, together with other low-level activity, and (v) for five pulsars, the timing activity is not due to a pure random walk process or resolved jumps. These results are discussed in the light of recent theories of mechanisms that may be responsible for pulsar timing noise.