We have carried out a multifrequency analysis of the radio variability of blazars, exploiting the data obtained during the extensive monitoring programs carried out at the University of Michigan Radio Astronomy Observatory (UMRAO, at 4.8, 8, and 14.5 GHz) and at the Metsähovi Radio Observatory (22 and 37 GHz). Two different techniques detect, in the Metsähovi light curves, evidence of periodicity at both frequencies for 5 sources (0224+671, 0945+408, 1226+023, 2200+420, and 2251+158). For the last three sources, consistent periods are found also at the three UMRAO frequencies and the Scargle (1982) method yields an extremely low false-alarm probability. On the other hand, the 22 and 37 GHz periodicities of 0224+671 and 0945+408 (which were less extensively monitored at Metsähovi and for which we get a significant false-alarm probability) are not confirmed by the UMRAO database, where some indications of ill-defined periods of about a factor of two longer are retrieved. We have also investigated the variability index, the structure function, and the distribution of intensity variations of the most extensively monitored sources. We find a statistically significant difference in the distribution of the variability index for BL Lac objects compared to flat-spectrum radio quasars (FSRQs), in the sense that the former objects are more variable. For both populations the variability index steadily increases with increasing frequency. The distribution of intensity variations also broadens with increasing frequency, and approaches a log-normal shape at the highest frequencies. We find that variability enhances by 20–30% the high frequency counts of extragalactic radio-sources at bright flux densities, such as those of the WMAP and Planck surveys. In all objects with detected periodicity we find evidence for the existence of impulsive signals superimposed on the periodic component.