We present a search for rings or arcs in the haloes of planetary nebulae (PNe). We discovered such structures in eight PNe, tripling the sample of PNe with known rings. This shows that, contrary to what was believed to date, the occurrence of mass loss fluctuations with timescales of 102-103 yrs at the end of the asymptotic giant branch phase (AGB) is common. We estimate a lower limit of the occurrence rate of rings in PN haloes to be ˜35%. Using these new detections and the cases previously known, we discuss the statistical properties of ring systems in PNe haloes. We estimate that the mass modulation producing the rings takes place during the last 10 000 or 20 000 yrs of AGB evolution. In PNe, the spacing between rings ranges from <0.01 pc to 0.06 pc, significantly larger than those seen in proto-PNe. This, together with the finding of a possible positive correlation of spacing with the post-AGB age of the nebulae, suggests that the spacing of the rings increases with time. These properties, as well as the modest surface brightness amplitudes of rings, are consistent with the predictions of the dust-driven wind instability model explored by Meijerink et al. (cite{Me03}), but do not immediately exclude other proposed models. Based on observations obtained at: the 2.5 INT telescope of the Isaac Newton Group and the 2.6 m NOT telescope operated by NOTSA in the Spanish Observatorio del Roque de Los Muchachos of the Instituto de Astrofísica de Canarias; the 3.5 m NTT and the 2.2 MPG/ESO at the European Southern Observatory in Chile; and the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA for NASA under contract NAS5-26555.