Some notes: Birds follow a slightly different power law and consequently live much longer. However, they do still follow a similar relationship.

Interesting exceptions in mammals are humans and (surprisingly) bats, both of which beat the curve pretty dramatically. Several mechanisms have been proposed for this exception including brain size and several specific proteins.

If anyone is interested in some more mechanistic or literature driven explanations, here is a good starting point http://www.ncbi.nlm.nih.gov/pmc/articles/PMC128563/