Well, I'm disgusted that PJ and co. even thought of putting this in the film. Clearly no one there had actually read the Silmarillion because if they had they would have noticed this:

(p.336, Akallabêth)

...and a third time, even as he laughed at his own thought, thinking what he would do now in the world, being rid of the Edain for ever, he was taken in the midst of his mirth, and his seat and his temple fell into the abyss. But Sauron was not of mortal flesh, and though he was robbed now of that shape in which he had wrough so great and evil, so that he could never again appear fair to the eyes of Men, yet his spirit arose out of the deep and passed as a shadow and a black wind over the sea, and came back to Middle-earth and to Mordor that was his home. There he took up again his great Ring in Brad-dur, and dwelt there, dark and silent, until he wrought himself a new guise, and image of malice and hatred made visible; and the Eye of Sauron the Terrible few could endure.

So there!

Many filmed scenes still remain unused, not included even in the Extended Editions. The main reason they weren't included was because they tended to change the plot from Tolkien's original storyline, therefore being unfaithful to the books.

-Additional footage from the Battle of the Last Alliance in the FotR Prologue.

-An obscure shot from the trailers of two Elven girls playing about in Rivendell.

-Dialogue from the Council of Elrond, such as Gandalf explaining how Sauron forged the One Ring.

-An attack by Moria Orcs on Lothlórien after the Fellowship leave Moria. Jackson replaced this with a more suspenseful entrance for the Fellowship. Much of the lost footage can be seen as promotional material on the FotR theatrical DVD and tie-in books, documentary footage on the Extended Editions, and cards.

-More Arwen footage, including a flashback scene of her first meeting with a beardless Aragorn (seen in the Two Towers teaser).

-Faramir having a vision of Frodo becoming like Gollum.

-Famous footage of Arwen at Helm's Deep, cut by Jackson during a revision to the film's plot. Foreshadowing this sequence were scenes where Arwen and Elrond visit Galadriel at Lothlórien (seen in The Two Towers teaser trailer). The scene was edited down to a telepathic communication between Elrond and Galadriel.

-Éowyn defending the refugees in the Glittering Caves from Uruk-hai intruders.

-An unknown scene displayed in The Two Towers preview of Éomer lowering a spear while riding his horse.

-A line of dialogue during the death of Saruman, in which he reveals that Wormtongue poisoned Théodred, giving further context as to why Wormtongue kills Saruman and Legolas in turn kills Wormtongue.

-A conversation between Elrond and Arwen in a library in Rivendell, after Arwen decides to wait for Aragorn. Elrond leaves saying "I cannot protect you anymore."

-The death of Gamling.

-Aragorn having his armor fitted during the preparations for the Battle of the Black Gate. This was the final scene filmed during principal photography.

-Sauron fighting Aragorn at the Black Gate. A computer-generated Troll was placed over Sauron due to Jackson feeling the scene was inappropriate. Sauron is also seen in a beautiful form as Annatar, giver of gifts.

-Also at the Black Gate sequence, Pippin was seen in the trailer holding a wounded Merry, a scene which takes place after the Battle of the Pelennor Fields upon Pippin discovering Merry under the mûmak.

-Further epilogue footage, including that of Legolas and Gimli, as well as Éowyn and Faramir's wedding and Aragorn's death and funeral.

Peter Jackson has stated that he would like to include some of these unused scenes in a future 'Ultimate Edition' home video release (probably High Definition) of the film trilogy. They will not be re-inserted into the movies but available for viewing separately. This edition will also include outtakes.