Recent progress in genomics and experimental biology has brought exponential growth of the biological information available for computational analysis in public genomics databases. However, applying the potentially enormous scientific value of this information to the understanding of biological systems requires computing and data storage technology of an unprecedented scale. The Grid, with its aggregated and distributed computational and storage infrastructure, offers an ideal platform for high-throughput bioinformatics analysis. To leverage this we have developed the Genome Analysis Research Environment (GNARE)--a scalable computational system for the high-throughput analysis of genomes, which provides an integrated database and computational backend for data-driven bioinformatics applications. GNARE efficiently automates the major steps of genome analysis including acquisition of data from multiple genomic databases; data analysis by a diverse set of bioinformatics tools; and storage of results and annotations. High-throughput computations in GNARE are performed using distributed heterogeneous Grid computing resources such as Grid2003, TeraGrid, and the DOE Science Grid. Multi-step genome analysis workflows involving massive data processing, the use of application-specific tools and algorithms and updating of an integrated database to provide interactive web access to results are all expressed and controlled by a "virtual data" model which transparently maps computational workflows to distributed Grid resources. This paper describes how Grid technologies such as Globus, Condor, and the Gryphyn Virtual Data System were applied in the development of GNARE. It focuses on our approach to Grid resource allocation and to the use of GNARE as a computational framework for the development of bioinformatics applications.