We soon will offer for download our implementation of the core calculation logic used by GREAT. The logic for associating regions with genes and calculating enrichments is also completely described in our Nature Biotechnology paper.
Our full GREAT application is very specific to our systems, which many hardcoded values and other dependencies on our setup. So, instead of providing a setup-specific application, we provide an implementation of the generally usable core calculation logic which can be used readily to build a version of GREAT that works on your system.
All of the data included in the GREAT ontologies is publicly available, and we provide links or references for every ontology. We do not currently offer our processed ontology data for download, but all data is available from the original sources. Additionally, the GREAT web tool offers numerous "Export" functions to save all ontology data as it pertains to your sets.