To place the Hermit Crabs and their relatives in taxonomic perspective let's do a/the usual rundown on their systematics starting from the:

Subphylum Crustacea:   

About 42,000 species of some of the most familiar arthropods; crabs, shrimps, lobsters, crayfish, wood-lice (sow-bugs, rolly-pollies, you know, terrestrial isopods, and aquatic, even parasitic marine ones). Many small members in fresh and marine habitats of importance in aquatic food chains. Primarily aquatic, mostly marine.

Some common characteristics of the crustaceans: 1) Their heads are more or less uniform with five pair of appendages: they have two pair of antennae (this feature is distinctive within the phylum); the third pair as opposing, biting, grinding mandibles. Behind the mandibles there are two pair of accessory feeding appendages, the first and second maxillae. 2) Their bodies trunks are composed of distinct segments covered by a chitinous exoskeleton strengthened by deposition of calcium salts. 3) Crustacean appendages are typically biramous (two major elements). 4) They typically have a carapace covering the trunk of their bodies. Enough of this detail. We'll cover this stuff in more general survey pieces of the mega-groups. On toward the lobsters.

A systematic resume of the Crustacea is necessarily large and complex. Allow me to semi-skirt around a full discussion here. The nine Classes that don't include our family of interest enclose the primitive cephalocaridans (C. Cephalocarida), the Class Branchiopoda (fairy shrimps, tadpole shrimps, water fleas (Daphnia); the Class Ostracoda, Class Copepoda (Anchor worm, Lernaea), Classes Mystacocarida, Branchiura, Tantulocarida, Remipedia, Cirripedia (barnacles), whew! & finally, our:

Class Malacostraca: 

Comprises almost three-fourths of all described species of crustaceans and most of the larger forms, such as crabs, lobsters, and shrimps. Characteristics: Trunks typically composed of 14 segments plus the telson ("tail"); the first 8 segments form the thorax, the last 6 the abdomen; all segments bear appendages. Four Superorders: Syncarida, Hoplocarida, Peracarida, and the one we want to talk about, the Eucarida.

Superorder Eucarida contains many of the large malacostracans. They have highly developed carapaces displaying fusion of all thoracic segments (the cepahalothorax). Eyes are stalked... Two living orders; the Euphausiacea (krill) and the:

Order Decapoda includes the familiar shrimps, crayfish, lobsters and crabs. This is the largest order of crustaceans with @10,000 species. Decapods are distinguishable from euphausiaceans and other malacostracans in that their first three pair of thoracic appendages, The remaining five pairs are legs (Decapoda= "ten feet"). Decapods are further divided into two Suborders, the Dendrobranciata, with "tree-like" branched gills, body laterally compressed..., eggs planktonic, nauplius as the first larval stage (as in Artemia, our brine shrimp), Infraorders, Sections, Superfamilies... See Barnes re their higher taxonomy.

Of animals that are Crabs ("false" and true) there are about eight thousand described species, with about 600 venturing into or living in freshwater. 

Infraorder Anomura, families of Hermit Crabs, Sand or Mole Crabs, Crab-like Crustaceans. Depressed carapaces, third pair of legs never chelate, fourth and fifth pair reduced....  Have a soft abdomen... live with bodies enclosed in discarded shells for the most part.

  Superfamily Galatheoidea         

Family Chirostylidae

Family Galatheidae (squat lobsters)

Family Porcellanidae (porcelain crabs)

   Superfamily Hippoidea     

Family Albueidae (mole crabs)

          Family Hippidae (sand crabs)

  Superfamily Paguroidea, have oval carapaces, usually asymmetrical. Live either in shells or with abdomen tucked underneath. First pair of legs as chelipeds. Includes the Hermit Crab genera: Pomatocheles, Petrochirus, Clibanarius, Coenobita (land Hermit Crab), Pagurus, Pylopagurus, Birgus (the Coconut Crab), Stone Crabs like Lithodes, Paralithodes (commercial King Crab of the North Pacific).

Best (most "Reef-Safe") Hermit Crab Species (though no carte-blanche guarantees) for Algae Control: Even these cannot be absolutely trusted with small fishes, invertebrates if hungry... and they too can be meals for... Puffers, Triggerfishes, Stomatopods (Mantis), Alpheids (Pistol Shrimp)...

Other Species of Hermits Sometimes

 Offered in the Interest that are TROUBLE: For (large) fish-only systems.

The Superfamily Paguroidea also includes Stone Crabs like Lithodes, Paralithodes (commercial King Crab of the North Pacific).

Care Notes:

If you use them, place about one, two small Hermits per actual gallon of your system. Use a mix of species and make sure and provide many "upgrade" homes (empty shells) for your Hermits to move to. 

Bibliography/Further Reading:

Systematics of Crustacea: http://www.dnr.state.sc.us/marine/sertc/Martin%20&%20Davis.pdf

http://www.marbef.org/data/ermstaxdetails.php?id=106685

http://animaldiversity.ummz.umich.edu/site/accounts/classification/Anomura.html#Anomura

Baensch, Hans & Helmut Debelius. 1994. Marine Atlas, v.1. MERGUS, Germany. 1215pp.

Brawer, Marc. 1970. Hermit Crabs. Marine Aquarist 1:6, 70.

Burgess, Warren E. 1974. Salts from the seven seas (on Hermits). TFH 11/74.

Debelius, Helmut. 1999. Crustacea of the World. Atlantic, Indian, Pacific Oceans. IKAN, Germany 321pp.

Friese, U. Erich. Crustaceans in the home aquarium. Hermit Crabs. TFH 4/85.

Hoover, John P. 1997. Hawaiian Hermit Crabs, pts. I,II. FAMA 9,10/97.

Jensen, Christopher. 1998. Red Legged Hermit Crab. FAMA 4/98.

Menten, Bob. 1980. The Hermit Crab. Marine scavenger- par excellence. TFH 11/80

Michael, Scott. 1998. Hermit danger. Some species of hermit crabs actually consider your fish their dinner. AFM 5/98.