As with many things in Tolkien, the exact number depends on which drafts you consider to be canoncanon; 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 ElurinElurín is more nuanced than Ask Middle-earth makes it seem.
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
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.
Eluréd and ElurinElurín
"Elboron" and "Elbereth" would later be replaces with "Elrun" and "Eldun", and eventually "Eluréd" and "Elurin"Elurín."
Dior [Beren and Luthien's]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 ElweElwë, the EluchilEluchíl.' 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 ElurinElurín. (the problem of ros)
Elrond and ElrosThe Problem of Half-Elves
Unlike ElurédThe OP specifically requested that half-elves be excluded. By that definition we're forced to exclude all but Amros and ElurinAmras, Elrond and Elros seem tosince all of the others have been twins fora Man somewhere in their entire textual history;ancestry1.
Although I don't want to speculate on the last mention of this is in a note addedreasons for the OP's restriction, there's no biological reason to The Tale of Yearsdistinguish 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:
528 Elros Elves and Elrond twin sons of Eärendil born.Men are evidently in biological terms one race, or they could not breed and produce fertile offspring – even as a rare event
History of Middle-earth XI The WarLetters of the JewelsJ.R.R. Tolkien Part 3: "The Wanderings of Húrin and other Writings not Forming Part of the *Quenta Silmarillion" Chapter V153: "The Tale of Years"To Peter Hastings (Draft). September 1954
The year wasI 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 changedin Letter 153). If that's true, then the choice of a half-elf to 532cast their lot in with the Eldar removes the distinction, but otherwise remains unchangedat least for our purposes. This isn't entirely surprising
1 Elrond and Elros are great-grandsons of Beren (through Elwing) and grandsons of Tuor, sinceson of Huor, of the House of Hador Elros was a late addition to the narrative(through Eärendil). Elladan and Elrohir have human ancestry through Elrond. Eluréd and Elurín, as mentioned in an above quote, are grandsons of Beren.