We present ab initio molecular dynamics studies on liquid water using density functional theory in conjunction with either dispersion-corrected atom-centered potentials or empirical van der Waals corrections. Our results show that improving the description of van der Waals interactions in DFT-GGA leads to a softening of liquid water's structure with higher mobility. The results obtained with dispersion-corrected atom-centered potentials are especially encouraging. In particular, the radial distribution functions are in better agreement with experiment, and the self-diffusion coefficient increases by more than three-fold compared with the one predicted by the BLYP functional. This work demonstrates that van der Waals interactions are essential in fine-tuning both structural and dynamical properties of liquid water.