The Sceptre of Annúminas:

An heirloom of the North Kingdom, this was the mark of royalty for Arnor. After the end of the North Kingdom it was kept in Rivendell. Elrond brought it to Minas Tirith and gave it to Aragorn at Midsummer in 3019.

Sting:

An elvish knife that served as a sword for Bilbo after the adventure in the Trolls cavern. Like Orcrist and Glamdring, it shone with a cold blue light when enemies were near. Sting could cut the webs of the Great Spiders with little effort, unlike even the swords of the Barrowdowns. After Frodo's sword was broken at the Fords, Bilbo gave Sting to him. Frodo gave Sting to Sam in Mordor, but was persuaded to take it back later. It is not known whether Frodo took Sting into the West, or left it with Sam.

The Silmarils:

Three jewels made by Fëanor. The Silmarils were made in such a way that they contained and shone with the light of the Two Trees. As Fëanor's greatest creation, the Silmarils were his pride and joy. Melkor lusted after them too, and plotted to steal them. This he accomplished after poisoning the Two Trees. The only remnant of the light of the Two Trees was in the Silmarils. Fëanor and his sons swore and oath to reclaim the Silmarils.
Then Fëanor swore a terrible oath. His seven sons leapt straightaway to his side and took the selfsame vow together, and red as blood shone their drawn swords in the glare of the torches. They swore an oath which none shall break, and none should take, by even the name of Ilúvatar, calling the Everlasting Dark upon them if they kept it not; and Manwë they named in witness, and Varda, and the hallowed mountain of Taniquetil, vowing to pursue with vengeance and hatred to the ends of the World Vala, Demon, Elf or Man as yet unborn, or any creature, great or small, good or evil, that time should bring forth unto the end of days, whoso should hold or take or keep a Silmaril from their possession.
Thus spoke Maedhros and Maglor and Celegorm, Curufin and Caranthir, Amrod and Amras, princes of the Noldor; and many quailed to hear the dread words. For so sworn, good or evil, an oath may not be broken, and it shall pursue oathkeeper and oathbreaker to the world's end. (S.97-98)

In the First Age of the Sun, Beren and Lúthien succeded in their quest to gain a Silmaril, though it cost both of them their lives. This is one of the most famous and heroic of the surviving tales of Middle-Earth.

At the end of the First Age, after the Great Battle in which Beleriand was destroyed, Maglor and Maehdros, the two surviving sons of Fëanor, took the Silmarils, but finding they burned their hands, Maedhros threw himself into a chasm full of fire and Maglor threw his into the sea. The Silmaril recovered by Beren and Lúthien was set in the sky as a star. It became known as Eärendil, the Evening Star.

The Seeing Stones:

The Palantíri of Arnor and Gondor.

The Seven:

The seven Rings given to the Dwarves.

The Sun:

The fruit that sprouted from Laurelin after the poisoning of the Two Trees by Melkor and Ungoliant. It was hallowed by Aule and guided by the Maia Arien. Another name for the Sun is Anor. In the traditions of both the Hobbits and the Eldar, the Sun is referred to as "she". Presumably, this is also true for Men, at least those who had had contact with the Elder Races.

The Hobbit
The Lord of the Rings
The Silmarillion
The Complete Guide to Middle-Earth by Robert Foster
The Unfinished Tales