This is a list of amphibians by family

Class Amphibia 
Total 6771 species

Order Anura  frogs and toads 
Total 5966 species
Suborder Archaeobatrachia
Family Alytidae - Painted Frogs or Disc-Tongued frogs, 12 species. 
Family Bombinatoridae - Fire Belly toads, 8 species
Family Leiopelmatidae - New Zealand primitive frogs, 6 species. 
Suborder Mesobatrachia
Family Megophryidae - Litter frogs or Short Legged toads, 156 species
Family Pelobatidae - European Spadefoot toads, 4 species
Family Pelodytidae - Parsley frogs, 3 species
Family Pipidae - Tongueless frogs or clawed frogs, 33 species
Family Rhinophrynidae - Mexican Burrowing Toad, 1 species
Family Scaphiopodidae - American spadefoot toads, 7 species
Suborder Neobatrachia
Family Allophrynidae, 1 species
Family Aromobatidae - 104 species
Family Arthroleptidae - Screeching frogs or squeakers, 140 species
Family Brachycephalidae - Saddleback toads, 51 species.
Family Brevicipitidae - 31 species
Family Bufonidae - True toads, 558 species
Family Calyptocephalellidae - 4 species
Family Centrolenidae - Glass frogs, 146 species
Family Ceratobatrachidae, 85 species
Family Ceratophryidae - 86 species
Family Ceuthomantidae - 4 species, split off from family Brachycephalidae
Family Craugastoridae - 115 species
Family Cycloramphidae - 105 species
Family Dendrobatidae - Poison dart frogs, 179 species
Family Dicroglossidae, 171 species
Family Eleutherodactylidae - 201 species
Family Heleophrynidae - Ghost frogs, 7 species
Family Hemiphractidae - 94 species
Family Hemisotidae - Shovelnose frogs, 9 species
Family Hylidae - Tree frogs, 901 species
Family Hylodidae - 42 species
Family Hyperoliidae - Sedge frogs or bush frogs, 209 species
Family Leiuperidae, 86 species
Family Leptodactylidae - Southern frogs or tropical frogs, 100 species
Family Mantellidae, 191 species
Family Micrixalidae - 11 species
Family Microhylidae - Narrow-mouthed frogs, 487 species
Family Myobatrachidae - Australian ground frogs, 85 species
Family Limnodynastidae, 43 species
Family Nasikabatrachidae - 1 species, formerly included in family Sooglossidae
Family Nyctibatrachidae - 17 species
Family Petropedetidae, 18 species
Family Phrynobatrachidae - 82 species
Family Ptychadenidae - 53 species
Family Pyxicephalidae - 68 species
Family Ranidae - True frogs, 347 species
Family Ranixalidae - 10 species
Family Rhacophoridae - Moss frogs, 321 species
Family Sooglossidae Seychelles Frog, 4 species.
Family Strabomantidae 569 species, removed from family Brachycephalidae

Order Caudata  salamanders 
Total 619 species
Suborder Cryptobranchoidea
Family Cryptobranchidae - Giant salamanders, 3 species
Family Hynobiidae - Asiatic salamanders, 55 species
Suborder Salamandroidea
Family Ambystomatidae - Mole salamanders, 37 species
Family Amphiumidae - Amphiumas or Congo eels, 3 species
Family Plethodontidae - Lungless salamanders, 418 species
 Subfamily: Spelerpinae, 36 species
Family Proteidae - Mudpuppies and Waterdogs, 6 species
Family Rhyacotritonidae - Torrent salamanders, 4 species
Family Salamandridae - True salamanders and newts, 89 species
Suborder Sirenoidea
Family Sirenidae - Sirens, 4 species

Order Gymnophiona or Caecilia 
Total 186 species
Family Caeciliidae - Common caecilians, 125 species. 
Family Ichthyophiidae - Fish caecilians, 50 species. 
Family Rhinatrematidae - Beaked caecilians, 11 species

Other websites
 Amphibian Species of the World
 AmphibiaWeb

Lists of animals