Determinations of beryllium abundance in stars, together with lithium, provide a key tool to investigate the so far poorly understood extra-mixing processes at work in stellar interiors. We measured Be in three open clusters,complementing existing Be surveys, and aiming at gathering a more complete empirical scenario of the evolution of Be as a function of stellar age and temperature. Specifically, we analyzed VLT/UVES spectra of members of NGC 2516, the Hyades, and M 67 to determine their Be and Li abundances. In the first two clusters we focused on stars cooler than 5400 K, while the M 67 sample includes stars warmer than 6150 K, as well as two subgiants and two blue stragglers. We also computed the evolution of Be for a 0.9 Mo star based on standard evolutionary models. We find different emprical behaviours for stars in different temperature bins and ages. Stars warmer than 6150 K show Be depletion and follow a Be vs. Li correlation while Be is undepleted in stars in the ~6150-5600 K range. NGC 2516 members cooler than 5400 K have not depleted any Be, but older Hyades of similar temperature do show some depletion. Be is severely depleted in the subgiants and blue stragglers. The results for warm stars are in agreement with previous studies, supporting the hypothesis that mixing in this temperature regime is driven by rotation. The same holds for the two subgiants that have evolved from the Li gap. This mechanism is instead not the dominant one for solar-type stars. We show that Be depletion of cool Hyades cannot simply be explained by the effect of increasing depth of the convective zone. Finally, the different Be content of the two blue stragglers suggests that they have formed by two different processes (i.e., collisions vs. binary merging).