Usually one sequences a new species because of some interesting aspects of its biology. In that sense, Istvan comment is very appropriate, but let me give you a few very quick examples of analyses that have been done with some vertebrate genomes.
In the analysis of the turkey genome, one of the questions was to address how much conserved sequence there is in avian genomes. These genomes being significantly shorter than mammalian ones, it wasn't clear if they contained the same amount or the same percentage of conserved sequence. Earlier, the zebra finch (the bird and not zebrafish the fish) was sequenced to discover genes involved in vocalization. One of the main points in the analysis not the gorilla genome was to look at the incomplete lineage sorting among human, chimpanzee and gorilla. With the sequence of the first teleost genome, one could look at the additional round of whole-genome duplication that happened in that lineage.
Those are a few examples of what people have been looking for in the new genome sequences. Again, there is no stereotypical analysis, as this depends very much on the biology and evolution of the species.