Crab on a Kos drachm
In addition to dolphins, the crab also figured prominently with ancients, who identified a star constellation (Cancer) in its shape along the sun's annual sky path, or ecliptic. Of the eventual 88 constellations these 12 had a special significance, being considered the "twelve monthly residences of Apollo", and as signs of the Zodiac were to further propel astrology. (The "uneven development" of astronomy and astrology over the last two millenia - scientifically a corollary of the sun's precession - resulted in the sun residing now in Gemini during the sign of Cancer, but that's another story...)
Some Greek city-states had a particular propensity for showing crabs on coins, the two classical examples being Akragas (later Roman Agrigentum) in Sicily, and the southeast Aegean island of Kos. Akragas - "the fairest of mortal cities" according to the famous 5th c. BC lyricist Pindar, and home of the famous scientist and philosopher Empedokles - lay actually on a plateau and cliff two miles inland, leaving apparently the impression of being "halfway between the sky and sea". This is might be one explanation for the eagle/crab design combination on many of its splendid coins, with the two symbolizing the divine rulers of these realms - Zeus and Poseidon, respectively. On the other hand, it is harder to decipher the crab's presence for Kos, in comparison to other themes popular on its coinage - those related to the veneration of Herakles, and later to that of the god of healing Asklepios, whose cult bloomed after the work of the native son Hippocrates.
Search for coins with crab themes.