Sometimes the claw is the only evidence. This is from one of the rock crab family, I think.
Asian Shore Crab (Hemigrapsus sanguineus). Another tentative ID.
Atlantic Blue Crab (Callinectes sapidus).
Flat-clawed Hermit (Pagurus pollicaris). (Gave this one its own post.)
Backyard and Beyond 
I found some leftovers like this on a cedar tree stump beside my pond many years ago. Likely a crawdad.