Eight optical and four radio observatories have been intensively monitoring the BL Lac object 0716+714 in the last years: 4854 data points have been collected in the UBVRI bands since 1994, while radio light curves extend back to 1978. Many of these data are presented here for the first time. The long-term trend shown by the optical light curves seems to vary with a characteristic time scale of about 3.3 years, while a longer period of 5.5-6 years seems to characterize the radio long-term variations. In general, optical colour indices are only weakly correlated with brightness. The radio flux behaviour at different frequencies is similar, but the flux variation amplitude decreases with increasing wavelength. The radio spectral index varies with brightness (harder when brighter), but the radio fluxes seem to be the sum of two different-spectrum contributions: a steady base level and a harder-spectrum variable component. Once the base level is removed, the radio variations appear as essentially achromatic, similarly to the optical behaviour. Flux variations at the higher radio frequencies lead the lower-frequency ones with week-month time scales. The behaviour of the optical and radio light curves is quite different, the broad radio outbursts not corresponding in time to the faster optical ones and the cross-correlation analysis indicating only weak correlation with long time lags. However, minor radio flux enhancements simultaneous with the major optical flares can be recognized, which may imply that the mechanism producing the strong flux increases in the optical band also marginally affects the radio one.