[luthien-elvenprincess]

In the case of Aragorn, I agree with Paavo and Lathspell, that Arwen was the temptation for Aragorn.
Paavo stated that if Galadriel offered Aragorn a spot on the ships to the Undying Lands, he could be with Arwen forever.
In ME, Aragorn could not marry Arwen until he became King Eleassar, due to Elrond's restriction. However, if he were indeed offered a place on the ship, he could bypass that restriction. But, he would then be renouncing his kingship along with his rights and responsibilities as Isildur's Heir, and the fate of ME would then be entirely hopeless.
If this were indeed the offering of Galadriel, Aragorn, by rejecting it, would have shown his true nobility and total unselfishness.
In the movies, it was made to seem as if Aragorn took up his kingship in order to save Arwen (her destiny was connected to the fate of the One Ring), but Tolkien gave Aragorn much noblier motives.