The best compilation of mermaid tales is Ruth Manning-Sanders' Book of Mermaids from 1968. The book contains sixteen tales retold by Manning-Sanders. She and Robin Jacques did twenty-five of these type of books together from 1962 to 1984.
In the foreword, she writes: "It may surprise you to learn that though many mermaids have tails and no legs, some have legs and no tail, and some have both legs and tails. ... However, there do seem to be more mermaids with tails than without them, and there are plenty of tailed mermaids (and mermen) swimming about in these stories, which, as we should expect, come mostly from countries with a long seaboard.And what are they like, these mermen and mermaids, not in looks but in character? On the whole, they are unchancy creatures, particularly the mermaids. You can't trust a mermaid even as far as you can see her."
The stories included are Sven and Lilli, The Four Abdallahs, The Lake Maiden, Merman Rosmer, The Geese and the Golden Chain, The Groach of the Isle of Lok, The Untidy Mermaid, The Magic Lake, The Comb, the Flute and the Spinning Wheel, The Magical Tune, The Lost Prince, The Three Mermaids, Rake Up!, The Kingdom of Ocean, Margrette, and Long John and the Mermaid. These stories are from all over the world, the Four Abdallahs being from the Arabian Nights, and Long John and the Mermaid being an American tale. All of these tales have been included in other books separately, like the Lilac Fairy Book, but to get them collected is a real treat.
This book is incredibly hard to find these days as it has been out of print for years. If you get the opportunity to pick it up, get it!