Currently, GREAT supports one recent assembly each of the well-annotated human (UCSC hg18) and mouse (UCSC mm9) genomes. GREAT can be expanded to include additional well annotated genomes (such as Zebrafish), and can also be expanded into less characterized genomes by carefully projecting annotations from well annotated ones. We hope to eventually expand the set of species we support.
GREAT only supports one assembly of the well-annotated human (hg18) and mouse (mm9) genomes. If you have genomic regions defined for a different species or assembly, you can use the UCSC LiftOver utility to convert to a supported assembly. The LiftOver works very well for within-species coordinate conversion (i.e. hg17 to hg18), but it can also be used as a best approximation of mapping regions in one genome to the orthologous regions of a genome for a different species.