I didn't know there were so many species of crabs until I started researching on the matter. Although this is not an exhaustive list, I will show you 41 types of crabs that are there in the world.

Some of the different types of crabs are:

Blue crab (Callinectes sapidus)
Dungeness crab (Metacarcinus magister)
Snow crab (Chionoecetes opilio)
King crab (Paralithodes camtschaticus)
Red crab (Gecarcoidea natalis)
Jonah crab (Cancer borealis)
Stone crab (Menippe mercenaria)
Mud crab (Scylla serrata)
Horseshoe crab (Limulus polyphemus) not a true crab, but often grouped with them
Spider crab (various species, including Macrocheira kaempferi)
Hermit crab (various species)
Fiddler crab (Uca species)
Coconut crab (Birgus latro)
Sally Lightfoot crab (Grapsus grapsus)
Velvet crab (Necora puber)
Pea crab (Pinnotheres species)
Green crab (Carcinus maenas)
Swimming crab (various species, such as Portunus pelagicus)
Coral crab (Trapezia species)
Ghost crab (Ocypode species)
Boxer crab (Lybia species)
Golden crab (Chaceon chilensis)
Decorator crab (various species)