Independent versifications
The versification of this passage from Donne predates the widespread use of the Internet, as you’ll see from the earliest examples below. Moreover, it looks as though multiple editors have independently decided to format the passage as verse. The evidence for this is that different editors have chosen different ways to break up the passage into lines. We would not expect this to happen if they were copying from some shared source. Here are two different eight-line versifications:
No man is an island, entire of itself;
every man is a piece of the continent, a part of the main.
If a clod be washed away by the sea,
Europe is the less, as well as if a promontory were,
as well as if a manor of thy friend’s or of thine own were:
any man’s death diminishes me, because I am involved in mankind,
and therefore never send to know for whom the bell tolls;
it tolls for thee.
Myrna Grant, ed. (1997) Poems for a Good and Happy Life, p. 104. Garden City: CrossAmerica.
No man is an island, entire of itself;
Every man is a piece of the Continent, a part of the main;
If a clod be washed away by the sea, Europe is the less,
As well as if a promontory were,
As well as if a manor of thy friend’s or of thine own were;
Any man’s death diminishes me, because I am involved in Mankind;
And therefore never send to know for whom the bell tolls;
It tolls for thee.
Mehmet Basci, ed. (2008). World Leaders’ Favourite Poems: a Book of Peace, p. 7. Cardigan: Parthian.
Two different nine-line versions:
No man is an island, entire of itself;
Every man is a piece of the continent, a part of the main.
If a clod be washed away by the sea, Europe is the less,
As well as if a promontory were;
As well as if a manor of thy friend’s or of thine own were;
Any man’s death diminishes me,
Because I am involved in mankind.
And therefore never send to know for whom the bell tolls;
It tolls for thee.
Jackie Morris, ed. (2006). Barefoot Book of Classic Poems, p.104. Cambridge: Barefoot Books.
No man is an island, entire of itself;
Everyman is a piece of the Continent, part of the main;
If a clod be washed away by the sea,
Europe is the less;
As well as if a promontary were;
As well as if a manor of thy friends, or of thine own were;
Any man’s death diminishes me, because I am involved in Mankind;
And therefore, never send to know for whom the bell tolls;
It tolls for thee.
Emeka Odumegwu-Ojukwu (1989). Because I am Involved, p. 111. Spectrum Books.
A seven-line version with an excision, identified by Peter Shor in comments:
No man is an island, entire of itself;
every man is a piece of the continent,
a part of the main;
… any man’s death diminishes me, because
I am involved in mankind;
and therefore never send to know for whom the bell tolls;
it tolls for thee.
Sarah Anne Stuart (1996). A Treasury of Poems, p. 221. New York: Galahad Books (1999). Ellipsis in original.
Manner of thine own
It is hard to trace the origin of these versifications because available search tools tend not to have any way of searching for line breaks, so that the rare versified versions of Donne’s text are buried among the common prose versions. However, if an editor happens to introduce a corruption at the same time as the versification, then the search tools become much more helpful. Here’s an example of such a corrupted text in the form of a fourteen-line versification:
No man is an island,
Entire of itself.
Each is a piece of the continent,
A part of the main.
If a clod be washed away by the sea,
Europe is the less.
As well as if a promontory were.
As well as if a manner of thine own
Or of thine friend’s were.
Any man’s death diminishes me,
Because I am involved in mankind.
Therefore, send not to know
For whom the bell tolls,
It tolls for thee.
Deborah Gaye, ed. (2010). Of Love and Hope, p. 152. London: Avalanche. Corruptions in bold.
Some of these changes might be defensible, but “manner” for “manor” and “thine friend” for “thy friend” are just embarrassing mistakes. But this version is rare and so more easily traceable. For example, here it appears in a novel:
The Sussex shore had been a haunt for smugglers. Towered over by the humps of the Seven Sisters and the knob of Beachy Head, pirates of old had hauled their contraband in through gaps in the cliff. The tales of these buccaneers provided J. M. Barrie with the inspiration for Captain Hook […] Lore like that cluttered Wyatt’s mind as he closed on the lonely cottage ahead. […] His epiphany was to recall John Donne, whose poem took on deeper meaning here at the rim:
No man is an island,
Entire of itself.
Every man is a piece of the continent,
A part of the main.
If a clod be washed away by the sea,
Europe is the less.
As well as if a promontory were.
As well as if a manner of thine own
Or of thine friend’s were.
Any man’s death diminishes me,
Because I am involved in mankind.
Therefore, send not to know
For whom the bell tolls,
It tolls for thee.
Michael Slade (2008), Crucified, pp. 230–231. Sutton: Severn House.
In the context of a novel, the errors are excusable, since we are told that the protagonist is recalling this “poem” from memory. In particular, the substitution of “manner of thine own” for Donne’s “manor … of thine own” is just the kind of trick that memory can play, because the protagonist’s recollections of stories of smugglers and pirates could have brought to mind a speech from Charles Kingsley’s Westward Ho!:
If it is ordained that thou shouldst advance the ends of the brotherhood by being shark-bitten, or flea-bitten, or bitten by sharpers, to the detriment of thy carnal wealth, or, shortly, to suffer any shame or torment whatsoever, even to strappado and scarpines, thou art bound to obey thy destiny, and not, after that vain Roman conceit, to choose the manner of thine own death, which is indeed only another sort of self-murder.
Charles Kingsley (1855). Westward Ho!, volume 2, p. 268. Cambridge: Macmillan.
On the Internet, this corruption can be traced using the Wayback Machine to this capture in July 2005, and on Google Books to A Purpose for Life: Service (2005) by Alexander Zax. Whether one of these is the original of the corrupted text, or whether both are copying from some yet older shared source, is impossible for me to say.