We have investigated the structure, adsorption, electronic states, and charge transfer of small water aggregates on the surface of a graphene layer using density functional theory. Our calculations were focused on water adsorbates containing up to five water molecules interacting with one and both sides of a perfect freestanding sheet. Different orientations of the aggregates with respect to the graphene sites were considered. The results show that the adsorption energy of one water molecule is primarily determined by its orientation, although it is also strongly dependent on the implemented functional scheme. Despite its intrinsic difficulties with dispersion interactions, the Perdew and Wang's exchange-correlation functional may be a viable alternative to investigate the adsorption of large molecular aggregates on a graphene surface. Although water physisorption is expected to occur in the regime of droplets, we found no induced impurity states close to the Fermi level of graphene interacting with small water clusters. In order to investigate the donor/acceptor tendency of the water clusters on graphene, we have performed a Bader charge analysis. Considering the charge transfer mechanism, we have noticed that it should preferentially occur from water to graphene only when the oxygen atom is pointing toward the surface. Otherwise, and in the case of larger adsorbed clusters, charge transfers systematically occur from graphene to water.