There are over 4,400 varieties of crabs, as mentioned in the accompanying article. Check this handy reference chart for a visual and text description of the most common edible types along with other crab terms you may come across in your culinary endeavors.

(blue crab graphic)
(blue crab molting shell photo)
Blue Crab
Its latin name, Calinectes sapidus, means "beautiful swimmer," and it is indeed a beautiful blue-green color. The most prolific species on the East Coast of the US, this is the crab which also gives us soft-shell crabs. They range in size from 3-1/2 inches up to 5-1/2 inches or more on the market. These crabs do turn the traditional reddish color when cooked.
(Dungeness crab graphic) Dungeness Crab
Latin name Cancer magister, this crab is found in coastal waters from Alaska, US to Baja, Mexico. This large crab usually weighs in from 1-3/4 to 4 pounds, and is brown to purple in color. It is named for the former small town of Dungeness on the Olympic Peninsula in Washington state, US, which first began commercially-harvesting the delicacy. Law requires the crab to be at least 6-1/4 inches long to be harvested, and only males can be taken. Prime season is in the winter months. The pink flesh is succulent and sweet.
(horseshoe crab graphic) Horseshoe Crab
Latin name Limulus polyphemus, this crab is named for its resemblance in shape to a horseshoe. It is considered a living fossil, tracing its roots back some 500 million years. It is found along the Atlantic coast from Nova Scotia to the Yucatan and along Asian coasts from Japan and the Philippines to India. And yes, they are indeed edible, although the ratio of meat to shell is small.
(king crab graphic) King Crab
Latin name Paralithodes camtschaticus, this giant crab is also often called "Alaskan King crab," "Japanese crab," and "Russian crab" due to its size, which can reach up to 25 pounds and measuring up to 10 feet. It may be large, but only about one-fourth is edible, primarily the legs and claws. Only males are harvested. The delicately-flavored meat is snowy white with a bright red outer edge.
(peekytoe crab graphic) Peekytoe Crab
These are Maine rock or sand crabs which were pretty much a throwaway by-product of lobster fishing before a brilliant marketing move changed their name to "peekytoes" around 1997. They are classified as Cancer irroratus, also known as bay crab and rock crab. You'll find full background information on this interesting and popular crab here.
(rock crab graphic) Rock Crab
Latin name Cancer quanbumi, it is found along the East coast of the US, living among rocks and in deep water. Its spindly legs make it resemble a spider, and is also known as "spider crab." "Snow crab," (Chionoecetes opilio) "tanner," and "queen crab" are also known as spider crabs.
(stone crab claw photo)
(stone crab claw photo)
Stone Crab
Latin name Menippe mercenaria, it is also called "moro" or "morro" crab. It has large, very hard claws that are prized for their meat. Most of the harvest comes from Florida, US, where it is a prized delicacy harvested from October 15 to May 15. Only the claws are eaten, so fishermen twist off one claw from crabs and toss them back to grow a new one. Crabs will regenerate their claws within 18 months. They are left with one claw to defend themselves. The law requires these claws to be boiled for 7 minutes and then either put on ice or frozen. The freezing process seems to remove an unpleasant iodine taste which is often noticed in the meat. To determine which claws have the most meat, they are floated in a tank of water, with the less meaty claws rising and being sold as "lights." To serve, the claws are cracked with a mallet and served cold with dipping sauces. Minimum size for claws is 2-2.75 ounces. The meat has a firm texture and a sweet, succulent flavor.

(crab photo) Here's a glossary of other crab terms you should be aware of when cooking crabs.

Back fin or Backfin Meat from the breast of the blue crab.
Ballie A female blue crab carrying eggs, also known as "bally" or "lemon-belly."
Buck A blue crab whose new shell has begun to harden too much, also known as "buckram," "papershell," and "buckler."
Buster A blue crab in the process of shedding its shell, also known as "peeler."
Comer A blue crab getting fat and ready to shed its shell.
Crab boil A packaged mixture of herbs and spices added to water in which crab is cooked. The blend usually includes mustard seeds, peppercorns, bay leaves, whole allspice, whole cloves, dried ginger pieces and red chiles.
Crab Butter This is the white-yellow fat inside the back of the shell of a large crab. It is considered a delicacy and is often added to dressings and sauces served with crab.
Crab Cake A mixture of crab, spices and binders flattened into patties and fried, originating in Maryland.
Crab Imperial An American favorite, this is a mixture of crabmeat covered with a white sauce, spooned into blue-crab shells, sprinkled with Parmesan cheese and/or bread crumbs and baked until golden brown.
Crab Louie or Louis A crabmeat salad made with hard-boiled eggs and lettuce topped with a dressing, whose origin is credited to numerous sources.
Jimmy A male blue crab.
Flake Small pieces of light and dark meat from the body and claws of the crab.
Lump Whole pieces of white meat from the body of the crab.
Rankpeeler A blue crab one to three days before it sheds its shell, particularly prized by chefs.
Roe The eggs of the crab, a delicacy required in some soups.
She-crab A female crab.
Soft-shell A blue crab that has shed its shell, before it has grown a new shell. The crab periodically sheds its shell to grow a larger one. Soft-shell crabs are in their prime from April to September. They are normally cooked whole and have no waste.
Sponge A female blue crab carrying eggs. Also called "punk" and "sook."