Thinking about the idea of Elves having low numbers overall, got me to wondering: as far as Tolkien's writing, could elves ever have twins?
As a "yes" answer, I need an example of twins (any of JRRT work). They must be full on Elves, not half-Men. As a "no" answer, has to be an explicit statement in his work stating Elves ALWAYS had one child at a time. Anything else is a "maybe, we don't know".
In a c.1959 text, published in The Nature of Middle-earth as "Time-scales", Tolkien elaborates on the frequency of elvish twins.
A greater number than four [children] was rare [for elves], though in the early days of the full vigour of the Eldar five or six children are recorded to have been born to one pair of spouses. Seven was wholly exceptional, and indeed among the High-elves only the case of Feänor is recorded. He had seven sons. The last two were twins: Amrod and Amras. Twins were very rare, and this is the only case recorded of the Eldar in the ancient histories, except for the twin sons, Eldún and Elrún, of Dior Eluchil, but he was half-elven. In later times (Third Age) Elrond had twin sons.
The Nature of Middle-earth - "Time-scales" - page 21-22
Roughly nine years later, in c.1968, Tolkien changed his mind about Dior's sons being twins:
He gave to his elder son the name Eluréd, that is said to have the same significance, but ended in the Bëorian word rêda 'heir'; to his second son he gave the name Elurín but his daughter the name Elwing.
[Christopher's commentary:] These names Eluréd and Elurín replace Eldún and Elrún (originally Elboron and Elbereth)', and the story that Dior's sons were twins had been abandoned.
The Peoples of Middle-earth - "The Problem of Ros" - page 369,372
So according to Tolkien's final conception it would seem that the only elvish twins were the following:
Tolkien says "twins were very rare", and so it is here probably safe to assume that these are in fact the only twins, not just the only ones who were main characters.
In the Silmarillion, Fëanor's youngest two sons, Amrod and Amras, are twins. Both of their parents are as Elvish as you could want. Fëanor had seven children—a number that was said to be utterly unprecedented for an Elf (before or since)—and this may be a part of that unprecedentedness. (Tolkien never portrayed any other Elf as having more than four children. In the published Silmarillion, Finarfin and his wife had five, but that's the result of Christopher Tolkien simplifying the family tree in a way he later regretted.)
There are a few other sets of Elvish twins, but all the ones I can think of have Men somewhere in their family tree. Dior and Nimloth had twin sons (Eluréd and Elurín) as did Elrond and Celebrían (Elladan and Elrohir).
As with many things in Tolkien, the exact number depends on which drafts you consider to be canon; there's somewhere between zero and four pairs. This answer is mostly in supplement to Wad Cheber's, but with canon sources added. However, the case of Eluréd and Elurín is more nuanced than Ask Middle-earth makes it seem.
But, easy ones first:
The canon is covered in my answer to a similar question.
The seven sons of Fëanor were Maidros [> Maedhros] the tall; Maglor a musician and mighty singer, whose voice was heard far over land and sea; Celegorn [> Celegorm] the fair, and Cranthir [> Caranthir} the dark; and Curufin the crafty, who inherited most of his father's skill of hand; and the youngest Damrod and Diriel [> Amrod and Amras], who were twin brothers alike in mood and face.
History of Middle-earth X Morgoth's Ring Part 3: "The Later Quenta Silmarillion" Chapter 1 "The First Phase" V "Of Eldanor and the Princes of the Eldalie"
And in the published Silmarillion (emphasis mine):
The seven sons of Fëanor were Maedhros the tall; Maglor the mighty singer, whose voice was heard far over land and sea; Celegorm the fair, and Caranthir the dark; Curufin the crafty, who inherited most his father's skill of hand; and the youngest Amrod and Amras, who were twin brothers, alike in mood and face. In later days they were great hunters in the woods of Middle-earth; and a hunter also was Celegorm, who in Valinor was a friend of Oromë, and often followed the Vala's horn.
The Silmarillion III Quenta Silmarillion Chapter 5: "Of Eldamar and the Princes of the Eldalië"
Elrond and Elros seem to have been twins for their entire textual history; the last mention of this is in a note added to The Tale of Years:
528 Elros and Elrond twin sons of Eärendil born.
History of Middle-earth XI The War of the Jewels Part 3: "The Wanderings of Húrin and other Writings not Forming Part of the *Quenta Silmarillion" Chapter V: "The Tale of Years"
The year was later changed to 532, but otherwise remains unchanged. This isn't entirely surprising, since Elros was a late addition to the narrative.
This is something Tolkien changed his mind on, repeatedly.
Initially, the sons of Dior were not twins; in The Genealogies, Tolkien writes:
Elboron son of Dior born 192; Elbereth his brother born 195
History of Middle-earth V The Lost Road and Other Writings Part 3 Appendix: "The Genealogies, The List of Names and the Second 'Silmarillion' Map"
"Elboron" and "Elbereth" would later be replaces with "Elrun" and "Eldun", and eventually "Eluréd" and "Elurín."
Later on, in a plot synopsis written while writing Narn i Chîn Húrin, he changed this:
500 Elrun and Eldun twin sons of Dior are born.
History of Middle-earth XI The War of the Jewels Part 3: "The Wanderings of Húrin and other Writings not Forming Part of the *Quenta Silmarillion" Chapter I: "The Wanderings of Húrin"
However, he changed his mind at least one more time, writing very late in his life:
Dior [Beren and Lúthien's] son, it is said, spoke both tongues: his father's, and his mother's, the Sindarin of Doriath. For he said: 'I am the first of the Peredil (Half-elven), but I am also the heir of King Elwë, the Eluchíl.' He gave to his elder son the name Eluréd, that is said to have the same significance, but ended in the Beorian word reda 'heir'; to his second son he gave the name Elurín.
History of Middle-earth XII The Peoples of Middle-earth Chapter 12: "The Problem of Ros"
The OP specifically requested that half-elves be excluded. By that definition we're forced to exclude all but Amros and Amras, since all of the others have a Man somewhere in their ancestry1.
Although I don't want to speculate on the reasons for the OP's restriction, there's no biological reason to distinguish between them. As Tolkien has noted on at least one occasion (Letter 153) that there's no biological distinction between Elves and Men, or at least that they're similar enough to breed:
Elves and Men are evidently in biological terms one race, or they could not breed and produce fertile offspring – even as a rare event
The Letters of J.R.R. Tolkien 153: To Peter Hastings (Draft). September 1954
I recall reading somewhere, though I can no longer remember the primary source, that the differences between Elves and Men are essentially spiritual, rather than biological (this is certainly the case with Elvish immortality, as Tolkien says later in Letter 153). If that's true, then the choice of a half-elf to cast their lot in with the Eldar removes the distinction, at least for our purposes.
1 Elrond and Elros are great-grandsons of Beren (through Elwing) and grandsons of Tuor, son of Huor, of the House of Hador (through Eärendil). Elladan and Elrohir have human ancestry through Elrond. Eluréd and Elurín, as mentioned in an above quote, are grandsons of Beren.
Elladan and Elrohir are described as twins. The word "twin" might not have been used, but they literally were "described" as twins.
"...and two tall men, neither young nor old. So much alike were they, the sons of Elrond, that few could tell them apart:..."
The Lord of the Rings, The Return of the King, Book V, Chapter II, The Passing of the Grey Company
Also in the Tale of Years, from Appendix B:
Year 130 Birth of Elladan and Elrohir, sons of Elrond.
The Lord of the Rings, The Return of the King, Appendix B, The Third Age
Pretty damn explicit. If Tolkien didn't want them to be twins he would have given them different birth years and not explicitly described them as being hard to tell apart. So I think it's super safe to assume that Elladan and Elrohir who were born in the same year, who looked suspiciously alike, and were never apart were twins.
According to the LotR wiki, there were at least 4 sets of Elf twins.
For more information, see this link to the "Ask Middle-earth" blog. Essentially, it confirms what Micah says in her excellent answer: most of the elf twins we know of are actually half-Elven. In fact, of the 12 known half-elves, 6 are twins! It is therefore likely that there is a correlation between being half-Elven and being/having twins.
There are actually a lot of twins in Middle Earth. More than seem statistically likely, but Tolkien never said if there was a specific reason for this. We meet four pairs of twins among the elves (all related), and two sets of twins among men.
Folcred and Fastred, one of the sets of twins among men, were the oldest sons of Folcwine, king of Rohan. In 2885 of the Third Age, Folcwine helped Gondor in their war with Harad. During a battle along the river Poros both Folcred and Fastred were killed, and buried on site. Their burial mound was later known as the Mound of the Twins. One of the elvish sets of twins also died together. Elured and Elurin, sons of Dior (and grandsons of Luthien) were abandoned in the forest to starve during the Kinslaying at Doriath, and were never seen again (they were only 6 years old at the time.)
In some accounts Amrod and Amras (sons of Feanor) also died together in battle, during the Kinslaying at the Havens of Sirion. However, other versions of the story give the pair a sadder fate. The two were very close, and called each other Ambarussa (“top-russet”, referring to their red hair). After Feanor and his people stole the ships from the Teleri and landed in Middle Earth, Amras slept on one of the ships. However, Feanor didn’t know this and didn’t wake him before setting fire to the ships later that night. Amrod only realized the next morning that his twin had died in the fire. Amrod was then killed towards the end of the age in the Kinslaying and the Havens...
Finally, it bears mentioning that, of the 12 peredhil (“half elves”), 6 of them are twins. Elured and Elurin, as descendants of Beren and Luthien, were half-elven. Their nephews, Elrond and Elros, were also half-elven, and Elrond’s sons Elladan and Elrohir were also half-elven. Whether this was intentional on Tolkien’s part or not is unknown, but I think it probably was, as a reflection of the duel-nature of a peredhel. Especially in the case of Elrond and Elros, where each twin literally represents one of the races of their ancestry. Elured and Elurin didn’t have a chance to make a choice about their nature, and we don’t know what Elladan and Elrohir chose. But maybe each set of twins ended up divided by fate?
