Desktop Grids have proved to be a suitable platform for the execution of Bag-of-Tasks applications but, being characterized by a high resource volatility, require the availability of scheduling techniques able to effectively deal with resource failures and/or unplanned periods of unavailability. In this paper we present a set of fault-aware scheduling policies that, rather than just tolerating faults as done by traditional fault-tolerant schedulers, exploit the information concerning resource availability to improve application performance. The performance of these strategies have been compared via simulation with those attained by traditional fault-tolerant schedulers. Our results, obtained by consider a set of realistic scenarios modeled after real Desktop Grids, show that our approach results in better application performance and resource utilization.