The tale of mermaids could likely have been inspired by the manatees and dugongs. The name for this order comes from the stories of the sirens, creatures that called out to sailors as described in the story of the Odessy.

Sirenians, which are sometimes called sea cows, are large mammals that spend their entire lives in the water. Unlike other large aquatic animals, like hippos, sirenians are not able to crawl out of the water. The species that make up this order are few. There were five living species of sirenians until the recent past. Now there are only four remaining species.
The following map shows the range of the living manatees

The four living species that make up this order are all endangered in the majority of their range.
A fifth species of sirenian is extinct. Steller's sea cows (genus Hydrodamalis) were huge sirenians (probably over 6000 kg, the size of African elephants!) related to dugongs. They lived in the Bering sea, where they fed on seaweed (no other mammal feeds exclusively on seaweed). Steller's sea cows were exterminated by sailors in the mid 1700's, shortly after their discovery. The remaining sirenians, manatees and dugongs, are seriously threatened by hunting, habitat degradation, and in the case of manatees, collisions with boats in the shallow coastal areas they prefer.
Recently we investigated the Florida Manatee, a subspecies of the West Indian Manatees, to learn more about what conservationists are doing to help protect these creatures.
Links:
[1] http://www.untamedscience.com/biodiversity/animals/chordates/mammals/manatees-and-dugongs/manatees/trichechus/west-indian-manatee
[2] http://www.untamedscience.com/biodiversity/animals/chordates/mammals/manatees-and-dugongs/dugongs/dugong/dugong