Anyone who has visited any brackish or marine environment has undoubtedly met some species of crabs. Some are commercial [such as Alaska king crabs, blue crabs, dungeness crabs, and snow crabs]. Others are interesting and/or the comics of the Crustaceans [hermit crabs and fiddler crabs]. Some are not crabs at all, although called crabs, like the horseshoe crab.

Here is a little on the taxonomy of the commercially edible Atlantic blue crab (Callinectus sapidus):

Superkingdom: Eukaryota All animals, plants, fungi, and protists.
Kingdom: Animalia Animals
Subkingdom: Metazoa Multicellular animals
Phylum: Arthropoda Jointed leg invertebrates
Subphylum: Crustacea Having a crustlike shell
Class: Malacostraca Shrimps, Crabs, Lobsters
Subclass: Eumalacostraca Have a 5-8-6 (head-thorax-abdomen) segment body plan
Superorder: Eucarida True shrimps
Order: Decapoda Ten legs
Suborder: Pleocyemata Gills lacking secondary branches and eggs carried on pleopods before hatching.
Infraorder: Brachyura Characterized by a reduced abdomen, folded beneath the cephalothorax, and inserted between the pereiopods or in a special cavity, which prevents it from impeding movements.
Section: Eubrachyura Press-button holding system, consisting of a prominence always on the fifth sternite and a socket always positioned on the sixth abdominal segment. Prevents abdomen from moving.
Subsection: Heterotremata Group in which the genital openings of the males are on the appendages and those of the females are on the thorax.
Superfamily: Portunoidea
Family: Portunidae Swimming crabs
Subfamily: Portuninae
Genus: Callinectes Greek word for beautiful swimmer (Calli = beautiful, Nectes = swimmer)
Species: Sapidus Latin word for savory
Scientific name: Callinectes sapidus
Authority: Rathbun, 1896

Common names: Atlantic blue crab.
Male crab called a jimmy or channler.
Mature female called a sook.
Young female called a sally crab or she crab.
Mature female carrying brood of eggs called a sponger or sponge crab.

All crabs will be the same listing down through the Order Decapoda which means ten legs.

Here is a list of pages, which you can go to, for information on certain crabs: (those in blue are ready and the others are in progress)

Blue crab

Dungeness crab

Fiddler crab

Hermit crab

Horseshoe crab--not a DECAPODA crab, i.e. not a true crab

King crab