The largest crab shells I run into on Maine beaches belong to Jonah Crabs (Cancer borealis). Along with Atlantic Rock Crabs (C. irroratus), these crustaceans are the source of native "Maine crabmeat" (see Maine Seafood Guide). Last year, I was fortunate to be given a hefty sum of freshly harvested Jonah Crab claws. I cooked and feasted on a pile of them and shared the rest with family and friends. My fingers were a bit sore at the end of the day from picking through the tough claw shells, but the sweet inner meat was well worth the effort.
Jonah Crabs can be separated from Atlantic Rock Crabs by examining the margin and overall shape of their shells. The Species ID card put out by the Gulf of Maine Research Institute includes drawings which highlight the differences.