The existence of fractal sets of DNA sequences have long been suspected on the basis of statistical analyses of genome data. In this article we identify for the first time explicitly the GA-sequences as a class of fractal genomic sequences that are easy to recognize and to extract, and are scattered densely throughout the chromosomes of a large number of genomes from different species and kingdoms including the human genome. Their existence and their fractality may have significant consequences for our understanding of the origin and evolution of genomes. Furthermore, as universal and natural markers they may be used to chart and explore the non-coding regions.