Unlike most theories on this list, this is not my own work; instead, it is a collation of three different theories proposed by various people on the Internet, and as such, will be sourced.
It has been known for a long time that three of the Nazgul were Numenoreans - but not which three. People long hypothesised that the Witch-King of Angmar should be one of the three, based on some quite ingenious arguments:
We know the Morgul Lord was the tallest of the Nine.
He spoke in quite a different style than say Khamul the Easterling. According to the Gaffer, Kamul had a foreign accent: "It was one of the Big Folk from foreign parts. He spoke funny."
The Easterling used simple sentences ("I come from yonder," "Have you seen Baggins?" "He is coming. He is not far away. I wish to find him. If he passes will you tell me? I will come back with gold.").
Compare it to the Witch-King's style: ‘Come not between the Nazgûl and his prey! Or he will not slay thee in thy turn. He will bear thee away to the houses of lamentation, beyond all darkness, where thy flesh shall be devoured, and thy shrivelled mind be left naked to the Lidless Eye." I bet here is a former High Numenorean speaking. (Ulairë Gordis, 16/10/2006)
Ultimately, direct evidence appeared in one of Tolkien's manuscripts: a statement that 'The name and origin of the Witch-king is not recorded, but he was probably (like the Lieutenant of Barad-dur) of Numenorean descent.' Based on this information, there are several theories about who, exactly, the Witch-King is. I will look at just three: the ones that state he was not just Numenorean, but from the actual royal house of Numenor, the Line of Elros.
Probably the weakest theory is that he was Isilmo, brother of Ruling Queen Tar-Telperiën. His son later became King as Tar-Minastir - but he himself did not, dying in S.A. 1731.
The main basis for this theory appears to be his name: it means 'man of the Moon', and the Witch-King later became ruler of Minas Ithil/Morgul, the Tower of the Moon. Herendil highlights quotes from 'The Stairs of Cirith Ungol', 'A Knife in the Dark', and 'The Palantir' which explicitly connect the Witch-King with moonlight.
One version of the theory states that '[Tar-Telperien] HAD to marry OR surrender the scepter to her brother. That was law. (Ancalime had to marry exactly because of the same reasons). But Telperien did neither - she kept the scepter and remained unmarried. Isilmo had all the reasons to complain.' (Ulairë Gordis, 18/10/2006). Another makes use of an error or mystery in Tolkien's timelines of Numenor: ' how Tar-Minastir sent a navy to Lindon in 1700
while Tar-Telperien was still was Queen (until 1731)' (Mark Crispin, 20/06/2002), and proposes that Isilmo was deliberately passed over in favour of making his son the Prince Regent. In either version, the snubbed Isilmo leaves Numenor, is given a Ring by Sauron, and slowly but surely became a Nazgul.
The main flaw with this theory is simply that, aside from the name, there is no evidence for it.
This next theory takes part of its evidence from a curious fact of the Rings - donning the One or the Nine renders your clothes invisible (like Bilbo), and those clothes remain on you if you become a wraith (Frodo saw the Nazgul clothed at Weathertop). Clothes put on you after you become a wraith, however - such as the cloaks of the Nazgul - stay visible. Therefore, when Frodo saw the Witch-King wearing a crown at Weathertop, the crown must have been his before he became a wraith - the crown of Angmar would have been a visible crown set on an invisible head, as we see at Minas Tirith.
If the Witch-King is a Numenorean, there is only one real way for him to wear a crown: for him to be a king of Numenor.
The second piece of evidence comes from another error/mystery in the Numenorean timelines:
Only at period from 1700 to 2251 of the Second Age Tolkien has a disorder with dates. And this disorder is INTENTIONAL. This is why Tolkien was strongly pointing on the fact that "Thought the dates given are often conjectural, especially for the Second Age, they DESERVES ATTENTION."(FOTR)
Next to him is growing the prince Atanamir, who in his behavior took a lot from his father. Seeing his father’s vigor and strength at the age, when it supposed to be the waning of abilities, made him yearn for longer life. Also his desire to cling to the life amplified even more by the fact that he in reality gained the scepter in 2251 at the decline of his long life and he did not want to end his kingship and his life willingly, like Numenorian tradition required. He became the Unwilling, the first Numenorian king who was clinging to his life even when the life was ending in dotage and infirmity. Unfortunately, after crossing the point of normal life span, (and according to different sources he lived 421 - 451 years), the final process of numenorian’s aging is very fast…
Why exactly him Tolkien made an Unwilling? Because in front of him Atanamir had a good example when the death was cheated. In consistent with the given by Tolkien dates in “The tale of the years”, Tar-Ciryatan lived 617 years and even after his official resignation in 2029 he continued to hold the scepter, being the ruler for 382 yeas, twice longer than his other predecessors, which is more than enough to make people begin to wonder. (Olmer, 30/05/2005)
Olmer is referring to the statement in the Appendices to the Lord of the Rings, that:
2251 Tar-Atanamir takes the sceptre. Rebellion and division of the Númenoreans begins. About this time the Nazgûl or Ringwraiths, slaves of the Nine Rings, first appear.
Christopher Tolkien thought that "2251" in the Appendices was a mistake, as in UT 2251 (or 2221) is the year of Atanamir's death. Olmer thinks this is no mistake, but a deliberate correction - an opening for a future nazgul story. Note that the very same entry speaks about the Nazgul's first appearance. (Ulairë Gordis, 17/10/2006)
If the 'mistake' was actually intentional, Tar-Ciryatan lived far longer than any other Numenorean - and clung to the scepter, somehow, after officially resigning two hundred years earlier.
The main flaws in this theory lie, first, in the fact that it relies entirely on an error, and secondly, that it requires Ciryatan to somehow convince the Numenoreans that he is dead, when they go to mummify his body.
An Unnamed Prince
We know when all the Nazgûl first appear together. That fact alone should be a flashing red light that Tolkien picked that point in the story because he himself had already worked through some back story that indicated where they’d come from. From that date, we can roughly work out when the last Man could first have gotten his Ring of Power, and then about when he was born, give or take a generation. That part isn’t a difficult exercise: you have to make some guesses about how long it takes to bake a Man into a wraith, and Tolkien himself never delves into such nasty details: I mean, who really wants to be a Necromancer? (It’s a dead-end job, right?) But we have this year in the Second Age, II 2251, “About this time the Nazgûl … first appear,” and it seems to me like a big signpost: “Ronald Tolkien has been working here." (Alcuin, 18/10/2006)
This theory, unlike the other two, doesn't make use of any errors in any of Tolkien's manuscripts; unfortunately, nor does it provide an actual name for the Witch-King. It is explained at length here by Alcuin, and can be summarised as follows:
The defeat of Sauron by the Eldar and Numenoreans in 1700 S.A. coincides very nearly with the Shadow falling over Numenor, which is first noted by Tolkien when Tar-Ciryatan forces his father to abdicate in S.A. 1837 - or even earlier, around 1800, when the Numenoreans began to establish their own realms in Middle-earth. If we accept the idea that the Witch-King was originally a man of noble purpose, the hundred-year gap corresponds nicely to how long he might take to 'fall' far enough to begin doing Sauron's will - specifically, to begin introducing the Shadow to Westernesse.
Tar-Minastir gives up the throne – unwillingly and under pressure from his own son – in II 1869. By this time, the Númenoreans have already established military fortifications along the west coast of Middle-earth, although neither Umbar nor Pelargir have yet been founded as the principal outposts of the Númenoreans in Middle-earth. In other words, someone has convince Tar-Ciryatan that he should be king in despite of his father’s wisdom, judgment, and good will, not to mention Númenorean law and custom. This person must have had access to Tar-Ciryatan, but more importantly, he must have had Tar-Ciryatan’s respect and been deep in his counsels. Moreover, this person must also have come under the sway of one of the Nine Rings – his personal power would have grown, his suasion and reason would seem stronger, he would likely have become unusually wealthy (and that likely from Middle-earth), so that he would seem more “respectable” than his peers. He would have to be someone close to Tar-Ciryatan, perhaps a member of the Council of the Scepter, someone who could whisper in private his poisons in the ear of the royal heir. This person would have to be a friend and a contemporary, probably a friend of Tar-Ciryatan’s youth. All these things strongly suggest a relative. This would suggest both Tar-Ciryatan’s scorn for “the yearnings of his father”, and his unseemly grasp for his father’s throne.
That would also give this person access to the young Tar-Atanamir, who was born in II 1800. Tar-Atanamir would naturally look up to his father’s friend and counselor, and he would give heed and credence to the lies this man would feed him, even when he was a young boy. If he were left in the care of this trusted friend – and relative – he would receive instruction against the Valar, and against the ban of the Valar. He would fail to teach his son Tar-Ancalimon to use Sindarin in his daily speech. And he would be unlikely to willingly lay down his life at the end, as even his father had done despite his other failings: he had learned to fear death and the Dark. He would be superstitious, and so would Tar-Ancalimon. (As above)
So far, so hypothetical. But the theory also states reasons why it may be true, rather than just proving the possibility:
It serves a strong literary purpose for the Lord of the Nazgûl to be a Númenorean prince of the Line of Elros. It explains the fall of the Shadow upon Númenor. It explains the heresy and decay that suddenly appears in the royal family after II 1800. It provides reason and context for the change in policy of the Númenoreans towards their kinsmen, the Men of the Twilight, left behind in Middle-earth. (As above)
...if this is true, then the Witch-king would have a stronger claim to the Númenórean throne than the Lords of Andúnië and the House of Elendil which descended from it; my answer to that is that with the rebellion of Ar-Pharazôn and the Akallabêth that descended upon Númenor as a result of his heresy, blasphemy, and impiety, the members of the House of Elros forever abrogated their ancient claim as kings of the Númenóreans, and it passed to their next-of-kin, the House of Valandil of Andúnië; but Ulairë Gordis is correct in saying that there is no reason for the Witch-king to recognize such an abrogation: in fact, he should have more strenuously pressed his claim.
That puts a whole different light on the wars of Angmar against Arnor and Minas Morgul against Minas Tirith, not to mention the crown on his head when the Witch-king broke the Gates of Minas Tirith in the Siege of Gondor, doesn’t it? (Alcuin, 16/10/2006)
The great irony of the fall and death of the Lord of the Nazgûl is that the people who killed him are people whom he despised. We need not attribute misogyny to the Lord of the Nazgûl: he despised Éowyn because although she was descended of the Edain, she was not a Númenorean. I purpose that he likely built his fortune as a living man and Númenorean prince by cruelly exploiting the people of Middle-earth, a pattern repeated by Tar-Ciryatan, Tar-Atanamir, Tar-Ancalimon, and their descendents. Of what significance could a woman of Middle-earth be to him? No wonder he uttered “a cry of hatred that stung the very ears like venom”: how dare such a lesser being raise her hand to smite him: descendent of Elros, prince of Númenor, king in Middle Earth, chief servant and prime instrument of Sauron? And as for Meriadoc the hobbit, he “heeded him no more than a worm in the mud.” It was the people of Middle-earth, long tormented and abused by the Black Númenoreans, and not the Dúnedain, who at last executed justice upon this ancient malefactor. (Alcuin's essay)
Which of these theories is correct? Any of them, or none - there is no real evidence that Tolkien ever considered the identity of the Witch-King. Which of the theories could be correct? Any of them - or none.