Living fossils
Lineages whose body plan has changed remarkably little over very long spans of time.
Atlantic Horseshoe CrabLimulus polyphemus- West Indian Ocean CoelacanthLatimeria chalumnae
Nautilus pompilius
Lingulid LampshellLingula anatina
TuataraSphenodon punctatus- Neoceratodus forsteri
About this list
The phrase is Darwin's and it is not quite right. None of these animals stopped evolving; their genomes have changed at ordinary rates, and living species are not identical to their fossil relatives. What is conserved is the external body plan, usually in lineages that found a stable habitat and stayed in it.
The coelacanth is the emblematic case: known only as Cretaceous fossils until a trawler landed one off South Africa in 1938.