Direct Numerical Simulations (DNS) of turbulent premixed flames burning hydrogen, synthetic gas and methane have been performed, relying on detailed chemical and transport models and taking into account volume viscosity. In this manner, it becomes possible to quantify the impact of this last contribution. It is shown that laminar flames are not modified by volume viscosity, while the local structure of turbulent flames may differ considerably when taking it into account. A noticeable impact is even observed on global flame properties. The modifications induced by the volume viscosity transport term are extremely small at first, but are sufficient to lead to completely different realizations at a later time due to the chaotic nature of turbulence. Noticeable modifications induced by volume viscosity are found for syngas as well as for hydrogen flames. For such hydrogen-containing fuels, the differences appear to remain unchanged when increasing the turbulent Reynolds number. On the other hand, turbulent flames burning methane show no significant impact due to volume viscosity. Since an accurate computation of the volume viscosity transport term is possible on available supercomputers, it is thus recommended to take it into account for detailed studies of turbulent flames burning hydrogen-containing fuels, in particular for DNS, while this term can be safely neglected for higher hydrocarbon flames.