There are two main reasons for this: Aragorn is part Maia himself (over Isildur , Elendil , Elros , Elwing , Lúthien and Melian , links from the LOTR Project family tree).
Isildur, Aragorn's ancestor, was the one who took the ring from Sauron in the war of the Last Alliance (with Narsil , the sword that was reforged and given to Aragorn before the end of the Ring War).
scifi.stackexchange.com/users/24826/Raidri supports Monica
In addition to the reasons cited in other answers, e.g., one of Aragorn's ancestors was a Maia, another one of his ancestors cut the Ring from Sauron's hand, he wields that same sword, reforged, there is another fear that Sauron had: Sauron does not know who has the Ring.
He suspects that Aragorn may have it, and in his pride, is attempting to overthrow Sauron to put himself in Sauron's place.
Aragorn, as a descendant of the Men of Númenor, armed with the One Ring, would be a truly terrifying foe.
Presumably, he would be able to control the Nazgûl, Orcs, and Trolls; he could persuade the men of Harad and Rhûn to change sides.
Sauron would be left without an army.
It is what he would do in our place.
That we would wish to overthrow him and have no one in his place, he has not considered.
That we should seek to destroy the Ring has not yet entered his darkest dreams.
(That quotation is from memory; I don't have the books with me.)
scifi.stackexchange.com/users/54975/Mike Harris
Because Aragorns ancestor Isildur was the one who cut the finger with the ring from Sauron.
And Aragorn is wielding the same reforged sword that did the deed.
scifi.stackexchange.com/users/42249/Thomas
Aragorn is the Heir of Isildur Being the rightful King to the thrones of Gondor 1 (and Arnor re-established), he had the potential to reunite the sundered Kingdoms of the Dúnedain: Arnor and Gondor, to oppose Sauron.
Then Aragorn, being now the Heir of Isildur, was taken with his mother to dwell in the house of Elrond; and Elrond took the place of his father and came to love him as a son of his own.
But he was called Estel, that is "Hope", and his true name and lineage were kept secret at the bidding of Elrond; for the Wise then knew that the Enemy was seeking to discover the Heir of Isildur, if any remained upon earth.
The bigger reason that Sauron was so fearful was that: Sauron (mistakenly) believed that Aragorn had the Ring and would use it against him '
Now Sauron knows all this, and he knows that this precious thing which he lost has been found again; but he does not yet know where it is, or so we hope.
And therefore he is now in great doubt.
For if we have found this thing, there are some among us with strength enough to wield it .
That too he knows.
For do I not guess rightly,
Aragorn, that you have shown yourself to him in the Stone of Orthanc? '
'
I did so
ere
I rode from the Hornburg,' answered Aragorn. '
I deemed that the time was ripe, and that the Stone had come to me for just such a purpose.
It was then ten days since the Ring-bearer went east from Rauros, and the Eye of Sauron, I thought, should be drawn out from his own land.
Too seldom has he been challenged since he returned to his Tower .
Though if I had foreseen how swift would be his onset in answer, maybe I should not have dared to show myself.
Bare time was given me to come to your aid.'
Therefore Sauron had all the more reason to fear Aragorn's power.
Though being a mortal Man, Aragorn 'wrenched' the Orthanc-stone against from Sauron's will .
That's definitely to be afraid of Aragorn.
I don't think that Aragorn having a very small amount of Maiar blood in him was the reason that Sauron feared him, as many of the other answers given seem to suggest.
By the time Aragorn was born, his Maiar blood was so diluted that it can be considered as irrelevant.
In this excellent answer Aragorn's Maiar blood percentage is calculated to be 0.000000000000000001355% .
1
: This is perfectly answered here .
scifi.stackexchange.com/users/82025/Mat Cauthon
Aragorn is the one man who can reunite the kingdoms of men (I mean Rohan and Gondor) and stand up to Sauron.
He can also summon the Men of the Mountain, but I do not think Sauron is aware of that.
scifi.stackexchange.com/users/54219/Eowyn12
Sauron manipulated the Palantíri to deceive, driving Saruman to treason and Denethor to despair, thus nobbling the strongest of his opponents.
Then up pops Aragorn.
He has the Palantír of Orthanc, so presumably he has already defeated Saruman while Mordor wasn't looking.
What's worse, he has the strength of will to take control of the Palantír, and the clear intention to claim the throne of Gondor, rally its people, and generally do all that Denethor could not.
All that scheming wasted!
scifi.stackexchange.com/users/48973/Anton Sherwood
He fears Aragorn (specifically Aragorn) because of a Prophecy of the Elves which fortells that the Heir of Isildur will encompass his destruction.
Sauron is a Maia but he is also dammned.
He fears the inevitable retribution for his evil.
scifi.stackexchange.com/users/59804/Marcus
I think most of the other answers have overlooked something else.
In addition to Sauron fearing him for his potential with the One Ring, which he thinks is Aragorns for the taking, there is this: He can command men, that is pretty much it.
In a fractured world (there are few and weak alliances)
he is the one man that can bring them together and put up a fight, even win, especially with the ring.
scifi.stackexchange.com/users/32445/arynaq
Sauron, formerly known as Mairon, fears Aragorn for reasons I do not know.  I especially do not understand, since Sauron is far more powerful than Aragorn even without the ring, as he is a Maia.  Why does Sauron fear Aragorn?
Why does Sauron fear Aragorn if he is a Maia?
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<the-lord-of-the-rings><tolkiens-legendarium>
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scifi.stackexchange.com/users/53038/Fingolfin
There are many potential reasons that Sauron would fear Aragorn, and any answer would be at least partially speculative. However, it is true that Aragorn is at least part Maia himself, and furthermore, Aragorn's ancestor was the one who took the ring from Sauron in the first place. Furthermore, Aragorn would be able to unite the kingdoms of men, and this combined with the One Ring would make him a very fearsome force. There are many reasons for Sauron to fear Aragorn, the main ones being that Aragorn has Maia ancestry, Aragorn's ancestor originally cut off the Ring, Aragorn is prophesied to be his doom, Aragorn may have the Ring and Aragorn can command men.
Because of Aragorn's Maia ancestry (Aragorn's ancestor Isildur had cut the Ring from Sauron's hand long ao) and because Aragorn has a sword forged from the original one used to cut off Sauron's ring finger. Sauron fears Aragorn because he can command men. Sauron fears Aragorn because he suspects that Aragorn may have the Ring.