Grid computing is becoming the natural way to aggregate and share large and heterogeneous sets of resources. However, grid development and acceptance hinge on proving that grids reliably support large communities of users, and their real applications. In this paper we assess the ability of existing grid infrastructures to provision resources for a class of applications with numerous potential users, namely the class of world-wide data-sharing services. For this purpose, we first analyze the requirements of this class of applications, and match them against the existing spare capacity in three existing large-scale grid environments, namely OSG/Grid3, NorduGrid, and CERN LCG. Having shown that the existing capacity is insufficient, we devise and assess through trace-based simulation five domainspecific scheduling policies. Our findings give evidence that grid technology could be successfully leveraged for worldwide data-sharing services, without impacting the level of service for the currently existing load.