Eukaryotic genome similarity relationships are inferred using sequence information derived from large aggregates of genomic sequences. Comparisons within and between species sample sequences are based on the profile of dinucleotide relative abundance values (The profile is rho*XY = f*XY/f*Xf*Y for all XY, where f*X denotes the frequency of the nucleotide X and f*XY denotes the frequency of the dinucleotide XY, both computed from the sequence concatenated with its inverted complement). Previous studies with respect to prokaryotes and this study document that profiles of different DNA sequence samples (sample size >/=50 kb) from the same organism are generally much more similar to each other than they are to profiles from other organisms, and that closely related organisms generally have more similar profiles than do distantly related organisms. On this basis we refer to the collection (rho*XY) as the genome signature. This paper identifies rho*XY extremes and compares genome signature differences for a diverse range of eukaryotic species. Interpretations on the mechanisms maintaining these profile differences center on genome-wide replication, repair, DNA structures, and context-dependent mutational biases. It is also observed that mitochondrial genome signature differences between species parallel the corresponding nuclear genome signature differences despite large differences between corresponding mitochondrial and nuclear signatures. The genome signature differences also have implications for contrasts between rodents and other mammals, and between monocot and dicot plants, as well as providing evidence for similarities among fungi and the diversity of protists.