Why did Sauron fear Aragons coronation?
 

Correct me if I'm wrong, or if have drawn to much from the movies as I have lost my (digital) copy of the trilogi, and the Silmarillon.

Gandalf says something like (and I'm pretty sure I'm qutoing, incorrectly, the movies here) "Sauron would rather raise Minas Tirith than see a king upon its throne." And Aragorn uses the palantiri to lure Sauron into attacking Minas Tirith before he is ready.

But what does Saouron fear? That Aragon has the ring? (as Aragorn is using the same palantiri as Pippin, who Sauron suspects have the ring).
Or that Gondor can withstand Mordor if they are but lead by a king?
Or that Aragorn will unite Gondor, Rohan and the remains of Arnor?
Or that he will unite all the enemies of Mordor, elves, dwarfs, men of dale and so on?

I think that's Peter Jackson "I can make boring 'ol Tolkien better"�™ revision.

In The Two Towers book Aragorn does say that to have realized that an Heir of Isildur was still living "was a blow to [Sauron's] heart".

Sauron naturally would have been shocked to discover that. His attention had been on Minas Tirith for so long that to have such an unexpected revelation threw him into turmoil. He had not forgotten that his previous defeat was at the hands of Isildur, and to have even "his" Palantír, with which he had confused or dominated two of his chief enemies having its link broken to the Orthanc-stone by the Heir filled him with fear. He was mainly worried, I think, that Aragorn would indeed claim the Ring, since in Sauron's mind someone so great could hardly resist it for long. Sauron may have even doubted that he could have recovered it from Aragorn forcibly (though I'm fairly certain he could have).

Aragorn's guess is that Sauron fears Isildur's heir and the sword of Elendil as powerful adversaries, knowing that he's reached a critical point in his plans:
I can't remember very much about the film universe, but if it does make the title a matter of fear rather than the man or the sword then it's a strange divergence from Tolkien, who places far more emphasis on personal worth than aristocratic rank. In the book, Sauron fears Aragorn, heir of Isildur, not the King of Gondor. Aragorn deliberately plays on this fear and doubt when he leads an army to the Morannon to draw Sauron's attention away from Frodo and Sam. The heir of Isildur is a likely candidate to take up the Ring against Sauron, and his leading a pitifully small army against Mordor is what Sauron would expect of a powerful leader falling under the Ring's domination.

Well Sauron has a great deal of hatred for Luthien's descedants as a whole. This is further increased by the Numenoreans stopping him in the Second Age. More fuel is added to the fire when the Numenoreans give him a humiliating defeat under Ar-pharazon. Then Elendil makes the last alliance and plays a big part in personally killing his body. Lastly to add insult to the wound Isildur takes his ring. So purely from a personal point he would be angry to find out that a descendant of Isildur still lived.

The other thing that would greatly worry him is the Heir of Isildur claiming the One Ring. Technically Aragorn has a legal right to the ring, which even Frodo acknowledges at the Council of Elrond. Whilst Aragorn has no possible hope of ever defeating Sauron in a personal battle, there is a chance he could unite the armies of the West against Sauron. He may even be able to gain the Black Numenoreans to his side. With such military power, just like the Numenoreans did, Aragorn could defeat Sauron's armies.

The last reason is that it is still a huge boost for the men of Gondor and strikes fear into the orcs. As Boromir put it the 'sword of Elendil would be a help beyond hope.' Similarly I think it would be a huge blow to the elves to see Narsil reforged.

I considered Aragorn himself and the sword of Elendil as great enemies of Sauron, however I felt that that was more dangerous to Sauron himself than to his armies. Of course it would cause fear among his armies but the differnence between Aragorn as king and Aragorn as "simply" the heir of Elendil would be small. However the stoming of Minas Tirith might just as well be to stop Aragorn from taking command of Gondors armies.

Yes this would be a classic case of where the film attributes significance to the wrong things for no essential narrative reason, which I think is one of the major pieces of evidence that the screenwriters literally didn't understand the words on the page. Sauron feared Aragorn and the Sword of Elendil mostly because he thought that Aragorn had the Ring - the Heir of Elendil with the Ring might be a formidable opponent militarily.

I think that a big part of Sauron's fear after the Palantir "conversation" was that he wat defeated in a battle of wills/minds by Aragorn. If being the heir of Isildur, a charismatic leader of Numenorian descent, and owner of Anduril and potentially of the Ring is not enough, this little trick does it. I imagine Sauron was seriously freaking out after a "mere mortal" beat him like that in his own field.

One thing I find curious that may bear on this is Aragorn's statement to Frodo on their meeting at Bree.

That suggests that Sauron was worried enough about the idea that an Heir of Isildur remained to have in some way been looking for evidence of such a person. Aragorn, of course, does not elaborate on the "traps", but it says something that even before the War of the Ring the Heir of Isildur was on Sauron's mind.

Possibly. But Aragorn was also the Chieftain of the Rangers; and even if Sauron had no idea that an heir of Isildur was alive, he must have been aware of the existence of the Rangers of Arnor. So it may be that the traps Aragorn refers to were set merely against the commander of the northern Dunedain, with no particular thought that he might be a claimant to Isildur's throne.

Would Sauron really have been that concerned about the Rangers, though? It doesn't look like he had any regard for Eriador in the Third Age, until he learned that was where his Ring had probably been taken. And if he or his servants knew of the Rangers, he should have observed they were guarding the Shire, and he shouldn't have been so clueless either about the location of Hobbits there.

But before Aragorn used the Palantír do we have any indication that Sauron was concerned about an Heir of Elendil?
That being said it seems to me that Aragorn's activities as Chieftain of the Northern Dúnedain, as Thorongil in Rohan and Gondor and his adventures in Rhûn and Harad must not have gone unnoticed even if Sauron wasn't aware of his lineage.

I think that Aragorn was referring to more general traps, against a Numenorian warrior brave enough to stick himself in Sauron's path. I doubt those traps were even aimed with the same person in mind, or for a greater purpose. They're just traps.

As for Sauron apprehending the heir of Isildur, I don't think he thought him dead as much as lost. I think he wasn't fooled by the destruction of Arnor into thinking that Isildur's line ended, but since the heir did not show a sign for so many generations he probably thought that the lineage was forgotten, or lost, or too mixed. He was still wary of a potential heir, or a Dunedain leader with enough lineage to be proclaimed King, but not as much as he would have been had he known the truth about Aragorn (which he became after he saw him in the Palantir).

Many competent generals waged war against Sauron over the millenia; some of them more formidable than Aragorn.

I've always thought that Sauron feared Aragorn's coronation as a sign of great change more than he feared Aragorn storming his gates.

A line from the Unfinished Tales section The Hunt For the Ring could contradict the idea of Sauron being interested in Aragorn personally.

That would seem to indicate that Sauron and his servants were simply vigilant for signs of an Heir of Isildur's return, though as Aragorn noted after his partial reveal to Sauron, the latter probably in his heart believed it wouldn't happen.