Natalie Angier, a science writer at the New York Times, has written a great feature article on the tuatara, a 'living fossil' that is the only remaining representative of its group, the sphenodontids. All other lizards and snakes are members of a group called the Squamata, which is distinct from the Sphenodontidae (see a reptile phylogeny at Tree of Life).
Some fun facts include their 'third eye' (the pineal eye), a primitive light-sensing organ in the center of their head which has been lost in most living reptiles, and their longevity - individuals in the wild may routinely reach 100 years or more, and continue to reproduce despite their advanced age.
Her article highlights research that shows how certain parts of the tuatara genome are evolving at a rapid rate, despite their apparent morphological 'stasis'. This questions our popular notion of what a 'living fossil' is - although they may appear to be quite similar to fossilized relatives from millions of years ago, we shouldn't forget that these organisms have had corresponding millions of years of evolution since that time, and so morphological stability may conceal other advanced specializations. It would be a mistake to think of these organisms as 'primitive' in the common sense of backward and inadequate.