The history of the ballad itself and its variants would make a long story, but suffice it to say that about 90% of the versions I know are based on Martin Carthy's 1966 version, released on his Second Album LP. Carthy shortened the lyrics to five well-rounded stanzas, and his slight variation of the source melody (an Irish air known as "The Croppy Boy" or Cailín Óg a Stór) has been universally carried forward. What follows is my own personal account of what I think are the best (and worst) versions, with a few comments on the more notable variations -- I hope that, should this ballad be one of your favorites, I might help you find further versions to enjoy, and avoid the (relatively few) awful ones.
As I say, Michael O Domhnaill's version, with his reedy yet potent voice, was the first I heard, and it remains my personal favorite. The well-known version by Pentagle is also a classic, and John Renbourn's guitar work on the tune is second to none. Another outstanding traditional version is John Walsh's from his album Aon Dó Trí (that's one two three in Irish); another by Take Two (the moniker of two Shropshire lads name of Dave Rolfe and Kevin Arnold) is also memorable. Special mention for over-use of echo should go to Sinéad O Connor's otherwise lovely recording, although rumor has it that an echo-free version is floating around the ether somewhere.
Rockier, or poppier versions also abound; that by the Glasgow-based Pearlfishers is the prize among these, though capable covers by the Tramps, Carmina, or Connie Dover are also appealing. For those who, at the other end of the spectrum, feel that anything more than a raspy a capella is too fancy, the Revels' version on their Homeward Bound CD is to my mind the best of the foke'sull school. I would warn, though, against the traditional version offered by "The Seamen's Institute" -- the tuneless warble of the unnamed singer on their version sounds rather like Sterling Holloway (the voice of Disney's Winnie the Pooh) after a night of excessive mead-guzzling.
One might well ask why a ballad which -- at least in part, and in some versions entirely -- is sung from Lady Franklin's point of view, why there have not been more versions by women. The gender imbalance has been greatly rectified in the digital age, with at least ten new recordings in the past decade. I'm personally fond of Jo Freya's version, with its pennywhistle and concertina accompaniment; Louise Killen's version, from her "Stars in the Morning" album, is also quite enchanting. The vocal treatment by the "Roots Quartet," alas, is far less felicitous; not only is the melody transposed into a modal version, but it's festooned with tinny harmonies that are reminiscent of a Roches outtake.
Lastly, there are a few instrumental-only versions, of which that recorded by Giuseppe Leopizzi and Roselina Guzzo is particularly rich and resonant. The melody has also been appropriated for other songs, among them Bob Dylan's "Bob Dylan's Dream" and David Wilcox's haunting "Jamie's Secret," which transposes the tale of Franklin's loss to the loss of a friend in the North Cascades of Washington State.
I'd be interested to hear from anyone who feels a favorite version has been slighted, or who disagrees with any of my calls!