The palantiri or ’those that watch from afar’ were the eight Seeing Stones made by Feanor in Aman. One of the eight known as the ’Masterstone’ has never left Aman, and resides in the Tower of Avallone upon Eressea. The remaining seven were given to the Numenorians as gifts from the Eldar.
At the time of the Downfall of Numenor, Elendil had the faithful load the Seven Stones on one of the nine ships they used to escape the destruction of Numenor. When the faithful arrived in Middle Earth, the Seven Stones were divided. Elendil took three, and his sons Isildur, and Anarion each took two.
The three Elendil took into his possession were placed at Emyn Beraid, Amon Sul (aka Weathertop), and Annuminas. The four taken collectively by his two sons were placed at Minas Ithil (later to become Minas Morgul), Minas Anor (later Minas Tirith), Orthanc, and Osgiliath. Tolkien refers to three of these Seven Stones being ’major’, and the other four as being ’minor’ Stones, and it’s in this way that I’ve attempted to address what happened to each.
The 3 ’major’ Stones are listed as being the Osgiliath-Stone, the Stone at Amon Sul, and the Stone that was located at Eymn Beraid. Tolkien lists the Osgiliath-Stone as being the ’Master Stone’ of the seven that were brought to M.E. This palantir is listed as being lost in T.A. 1437 in the Anduin when Osgiliath was burned during the civil war of the Kin-strife (appendices of ROTK, page 405). The Stone of Amon Sul was lost in T.A. 1975 in the shipwreck of Arvedui (along with the Stone of Annuminas). The Stone that was located at Eymn Beraid (or Elendil-Stone), was unlike the others, and was not in accord with them. This Stone looked only to the sea. Kept extremely secret it was never lost, and was maintained in a tower guarded by Cirdan, and the Elves of Lindon. It is said that Cirdan put this Stone aboard Elrond’s ship when he left for the Undying Lands.
Tolkien lists the four ’minor" Stones as being the Stone of Orthanc, the Anor-Stone, the Ithil-Stone, and the Stone of Annuminas. The Ithil-Stone was captured in T.A. 2002 by Sauron’s forces in the fall of Minas Ithil. This is the Stone that Sauron possessed during the time of The War of the Ring. This Stone was never found again, and it's believed that this Stone perished in the ruin of Barad-dur. The Stone of Annuminas, as already briefly mentioned, was lost in T.A. 1437 with the Stone from Amon Sul. After the destruction of Amon Sul by Angmar in T. A. 1409, both Stones were then placed at Fornost, where the King of Arthedain lived, it was in this way that the two were together when they were lost in the shipwreck of Arvedui.
The Stone of Orthanc, and the Anor-Stone were never lost (for more precise info, please see the chapter on The Palantiri in UT). The Anor-Stone resided in Minas Tirith (and was the one used by Denethor). Proof that the Anor-Stone survived the burning of Denethor is provided on page 131 of ROTK;
And it was said that ever after, if any man looked in that Stone, unless he had a great strength of will to turn it to other purpose, he saw only two aged hands withering in flame.
Obviously, the Orthanc-Stone resided at the tower of Orthanc. Forgotten about for quite sometime (though not by Saruman), this is the Stone that both Saruman, and Aragorn gazed into. Since Aragorn was their rightful heir, both of these Stones were in his possession once he became king (although, as we know, Aragorn possessed the Orthanc-Stone before he was actually crowned the new King of Gondor).