Answer:
According to wiki species, there are 38 species of dolphins that belong to the family Delphinidae or oceanic dolphins, plus five species of River Dolphins.
However, a new species was discovered in 2011 giving a new total of 44 species.
Family Delphinidae, oceanic dolphins:
- Long-Beaked Common Dolphin, Delphinus capensis
- Short-Beaked Common Dolphin, Delphinus delphis
- Bottlenose Dolphin, Tursiops truncatus
- Indo-Pacific Bottlenose Dolphin, Tursiops aduncus
- Northern Rightwhale Dolphin, Lissodelphis borealis
- Southern Rightwhale Dolphin, Lissiodelphis peronii
- Tucuxi, Sotalia fluviatilis
- Costero, Sotalia guianensi
- Indo-Pacific Hump-backed Dolphin, Sousa chinensis
- Chinese White Dolphin (the Chinese variant), Sousa chinensis chinensis
- Atlantic Humpbacked Dolphin, Sousa teuszii
- Atlantic Spotted Dolphin, Stenella frontalis
- Clymene Dolphin, Stenella clymene
- Pantropical Spotted Dolphin, Stenella attenuata
- Spinner Dolphin, Stenella longirostris
- Striped Dolphin, Stenella coeruleoalba
- Rough-Toothed Dolphin, Steno bredanensis
- Chilean Dolphin, Cephalorhynchus eutropia
- Commerson’s Dolphin, Cephalorhynchus commersonii
- Heaviside’s Dolphin, Cephalorhynchus heavisidii
- Hector’s Dolphin, Cephalorhynchus hectori
- Risso’s Dolphin, Grampus griseus
- Fraser’s Dolphin, Lagenodelphis hosei
- Atlantic White-Sided Dolphin, Lagenorhynchus acutus
- Dusky Dolphin, Lagenorhynchus obscurus
- Hourglass Dolphin, Lagenorhynchus cruciger
- Pacific White-Sided Dolphin, Lagenorhynchus obliquidens
- Peale’s Dolphin, Lagenorhynchus australis
- White-Beaked Dolphin, Lagenorhynchus albirostris
- Australian Snubfin Dolphin, Orcaella heinsohni
- Irrawaddy Dolphin, Orcaella brevirostris
- Melon-headed Whale, Peponocephala electra
- Killer Whale (Orca), Orcinus orca
- Pygmy Killer Whale, Feresa attenuata
- False Killer Whale, Pseudorca crassidens
- Long-finned Pilot Whale, Globicephala melas
- Short-finned Pilot Whale, Globicephala macrorhynchus
- Guiana dolphin, Sotalia guianensis
River Dolphins
- Boto (Amazon River Dolphin), Inia geoffrensis
- Chinese River Dolphin (Baiji), Lipotes vexillifer (considered functionally extinct)
- Ganges River Dolphin, Platanista gangetica gangetica and Indus River Dolphin, Platanista gangetica minor
- La Plata Dolphin (Franciscana), Pontoporia blainvillei
- Indus River Dolphin, Platanista gangetica minor
New Species
During 2011, a new species of Dolphin was discovered, adding one to the numbers above: Burrunan Dolphin, Tursiops australis.