Ever since Charles Darwin coined the term "living fossil," it's been bandied around very loosely. One creature that desrves the label more than most is the coelacanth, which hasn't changed a whole lot in 300 million years. Sequencing its DNA tells us why: its genes don't evolve very fast. Those of reptiles and mammals evolve at twice this rate. Why? We're not sure.
We're not sure about this critter either - the immortal jellyfish. When it ages, it collapses into a pile of goo and starts the life cycle over again. James Cameron never imagined anything so weird on Pandora.